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\(\mathrm{a}, \mathrm{b}, \ldots, \mathrm{e}\) are positive integers
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\(\mathrm{a}, \mathrm{b}, \ldots, \mathrm{e}\) are positive integers\(\mathrm{a}, \mathrm{b}, \ldots, \mathrm{e}\) are positive integers abcde \(=a+b+c+d+e\) \(\max (\max (a, b, c, d, e))=?\) ...
by Pieter Gold Status
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asked in Mathematics May 5
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Solve the equation \(\sqrt{x+18}=x-2\)
1 answer 29 views
Solve the equation \(\sqrt{x+18}=x-2\)Solve the equation \(\sqrt{x+18}=x-2\) ...
by Pieter Gold Status
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asked in Mathematics May 2
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What questions should I ask when determining real user needs for product design?
1 answer 50 views
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How do I do this mentally and quickly? If \(512=x^2-y^2\) and \(c\) and \(y\) are positive triangular numbers, then \(x=\) ?
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If \(x^{*} y=-10\), what is the value of \(\left(4^{*} 4\right) * 3\) ?
0 answers 85 views
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If \(f(x) \in C^{n+1}[a, b]\), then
1 answer 66 views
If \(f(x) \in C^{n+1}[a, b]\), thenIf \(f(x) \in C^{n+1}a, b\), then ...
by MathsGee Platinum
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asked in Mathematics Feb 20
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What is global warming?
1 answer 59 views
What is global warming?What is global warming? ...
by MathsGee Platinum
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asked in Geography & Environment Feb 19
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How do we know global warming is real?
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How do we know global warming is real?How do we know global warming is real? ...
by MathsGee Platinum
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asked in Geography & Environment Feb 19
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If \(x=-3\) and \(y=4\) find the value of: \[ x(3 x+4 y) \]
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Simplify. \(-3+8-1-7+12+1\)
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Simplify. \(-3+8-1-7+12+1\)Simplify. \(-3+8-1-7+12+1\) ...
by Pieter Gold Status
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asked in Mathematics Feb 5
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What is Real Time Bidding (RTB) in online advertising?
1 answer 49 views
What is Real Time Bidding (RTB) in online advertising?What is Real Time Bidding (RTB) in online advertising? ...
by MathsGee Platinum
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asked in Advertising & Marketing Feb 3
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Solve \(\sqrt{14+17 x-2 x^{2}}=x+2\)
1 answer 50 views
Solve \(\sqrt{14+17 x-2 x^{2}}=x+2\)Solve \(\sqrt{14+17 x-2 x^{2}}=x+2\) ...
by MathsGee Platinum
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asked in Mathematics Jan 31
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With regards to climate targets, what is the difference between "Real Zero" and the "Net Zero"?
0 answers 52 views
With regards to climate targets, what is the difference between "Real Zero" and the "Net Zero"?With regards to climate targets, what is the difference between "Real Zero" and the "Net Zero"? ...
by MathsGee Platinum
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asked in Geography & Environment Jan 28
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How do I use maths to solve real life problems?
1 answer 86 views
How do I use maths to solve real life problems?How do I use maths to solve real life problems? ...
by MathsGee Platinum
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asked in Mathematics Jan 28
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What is an n-tuple of real numbers?
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What is an n-tuple of real numbers?What is an n-tuple of real numbers? ...
by MathsGee Platinum
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asked in Mathematics Jan 26
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What is a zero vector?
1 answer 58 views
What is a zero vector?What is a zero vector? ...
by MathsGee Platinum
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asked in Mathematics Jan 26
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Give a real life and practical application of linear combinations of vectors
1 answer 51 views
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What is Simpson's paradox?
1 answer 62 views
What is Simpson's paradox?What is Simpson's paradox? ...
by MathsGee Platinum
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asked in Data Science & Statistics Jan 24
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Let \(S_{N}:=1+\frac{1}{2}+\cdots+\frac{1}{N}\). Find an estimate for \(N\) so that \(S_{N}>100\).
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A tridiagonal matrix is a square matrix with zeroes everywhere except on the main diagonal and the diagonals just above and below the main diagonal.

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Let \(A\) be a square matrix of real numbers whose columns are (non-zero) orthogonal vectors.
0 answers 189 views
Let \(A\) be a square matrix of real numbers whose columns are (non-zero) orthogonal vectors.Let \(A\) be a square matrix of real numbers whose columns are (non-zero) orthogonal vectors. a) Show that \(A^{T} A\) is a diagonal matrix - whose in ...
by MathsGee Platinum
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asked in Mathematics Jan 21
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Let \(A\) be a square matrix and let \(\|B\|\) be any norm on matrices [one example is \(\left.\|B\|=\max _{i, j}\left|b_{i j}\right|\right]\).
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Let \(A\) be a square matrix. In the following, a sequence of matrices \(C_{j}\) converges if all of its elements converge.
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A \(3 \times 3\) real matrix need not have any real eigenvalues.
0 answers 87 views
A \(3 \times 3\) real matrix need not have any real eigenvalues.True or False - and Why? a) A \(3 \times 3\) real matrix need not have any real eigenvalues. b) If an \(n \times n\) matrix \(A\) is invertible, then ...
by MathsGee Platinum
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asked in Mathematics Jan 21
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For non-zero real numbers one uses \(\frac{1}{a}-\frac{1}{b}=\frac{b-a}{a b}\). Verify the following analog for invertible matrices \(A, B\) :
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Show that \(\operatorname{trace}(A B C)=\operatorname{trace}(C A B)=\operatorname{trace}(B C A)\).
0 answers 142 views
Show that \(\operatorname{trace}(A B C)=\operatorname{trace}(C A B)=\operatorname{trace}(B C A)\).Let \(A, B\), and \(C\) be any \(n \times n\) matrices. a) Show that \(\operatorname{trace}(A B)=\operatorname{trace}(B A)\). b) Show that \(\operator ...
by MathsGee Platinum
(118,646 points)
asked in Mathematics Jan 21
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Let \(L: V \rightarrow V\) be a linear map on a vector space \(V\).
0 answers 48 views
Let \(L: V \rightarrow V\) be a linear map on a vector space \(V\).Let \(L: V \rightarrow V\) be a linear map on a vector space \(V\). a) Show that \(\operatorname{ker} L \subset \operatorname{ker} L^{2}\) and, more g ...
by MathsGee Platinum
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asked in Mathematics Jan 21
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Every real upper triangular \(n \times n\) matrix \(\left(a_{i j}\right)\) with \(a_{i i}=1, i=1,2, \ldots, n\) is invertible. Proof or counterexample.

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Let \(A\) be a real matrix, not necessarily square.
0 answers 197 views
Let \(A\) be a real matrix, not necessarily square.Let \(A\) be a real matrix, not necessarily square.   a) If \(A\) is onto, show that \(A^{}\) is one-to-one. b) If \(A\) is one-to-one, show ...
by MathsGee Platinum
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asked in Mathematics Jan 21
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Find the dimension of \(A\) considered as a real vector space.
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Find the dimension of \(A\) considered as a real vector space.Consider the two linear transformations on the vector space \(V=\mathbf{R}^{n}\) : \(R=\) right shift: \(\left(x_{1}, \ldots, x_{n}\right) \rightarrow ...
by MathsGee Platinum
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asked in Mathematics Jan 21
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Show that \(\mathcal{L}\) and \(\mathcal{R}\) are linear spaces and compute their dimensions.
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Show that \(\mathcal{L}\) and \(\mathcal{R}\) are linear spaces and compute their dimensions.Say \(A \in M(n, \mathbb{F})\) has rank \(k\). Define \ \mathcal{L}:=\{B \in M(n, \mathbb{F}) \mid B A=0\} \quad \text { and } \quad \mathcal{R}:=\{C ...
by MathsGee Platinum
(118,646 points)
asked in Mathematics Jan 21
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Give an example of a square real matrix that has rank 2 and all of whose eigenvalues are zero.
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Let \(V, W\) be two-dimensional real vector spaces, and let \(f_{1}, \ldots, f_{5}\) be linear transformations from \(V\) to \(W\).
0 answers 188 views
Let \(V, W\) be two-dimensional real vector spaces, and let \(f_{1}, \ldots, f_{5}\) be linear transformations from \(V\) to \(W\).Let \(V, W\) be two-dimensional real vector spaces, and let \(f_{1}, \ldots, f_{5}\) be linear transformations from \(V\) to \(W\). Show that there ex ...
by MathsGee Platinum
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asked in Mathematics Jan 21
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Let \(A\) be a square real (or complex) matrix. Then \(A\) is invertible if and only if zero is not an eigenvalue. Proof or counterexample.
0 answers 168 views
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Let \(A\) be a real square matrix satisfying \(A^{17}=0\).
0 answers 156 views
Let \(A\) be a real square matrix satisfying \(A^{17}=0\).Let \(A\) be a real square matrix satisfying \(A^{17}=0\). a) Show that the matrix \(I-A\) is invertible. b) If \(B\) is an invertible matrix, is \(B ...
by MathsGee Platinum
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asked in Mathematics Jan 21
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Find a real \(2 \times 2\) matrix \(A\) (other than \(A=I\) ) such that \(A^{5}=I\).
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Let \(U\) and \(V\) both be two-dimensional subspaces of \(\mathbb{R}^{5}\), and let \(W=U \cap V\). Find all possible values for the dimension of \(W\).

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Let \(C(\mathbb{R})\) be the linear space of all continuous functions from \(\mathbb{R}\) to \(\mathbb{R}\).
0 answers 137 views
Let \(C(\mathbb{R})\) be the linear space of all continuous functions from \(\mathbb{R}\) to \(\mathbb{R}\).Let \(C(\mathbb{R})\) be the linear space of all continuous functions from \(\mathbb{R}\) to \(\mathbb{R}\). a) Let \(S_{c}\) be the set of different ...
by MathsGee Platinum
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asked in Mathematics Jan 20
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For which real numbers \(x\) do the vectors: \((x, 1,1,1),(1, x, 1,1),(1,1, x, 1),(1,1,1, x)\) not form a basis of \(\mathbb{R}^{4}\) ?
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Which of the following sets are linear spaces?
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Which of the following sets are linear spaces?Which of the following sets are linear spaces? a) \(\left\{X=\left(x_{1}, x_{2}, x_{3}\right)\right.\) in \(\mathbb{R}^{3}\) with the property \(\lef ...
by MathsGee Platinum
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asked in Mathematics Jan 20
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The complex number $i^{19}$ is equal to
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The complex number $i^{19}$ is equal toThe complex number $i^{19}$ is equal to   A) 1 B) $-1$ C) i D) $-i$ E) none of the above ...
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asked in Mathematics Jan 13
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