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Let \(L: V \rightarrow V\) be a linear map on a vector space \(V\).
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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 ...
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asked in Mathematics 54 seconds ago
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Let \(A\) be a real matrix, not necessarily square.
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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 ...
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asked in Mathematics 11 minutes ago
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Give an example of a linear transformation \(L: V \rightarrow V\) (or show that there is no such transformation) for which:
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Give an example of a linear transformation \(L: V \rightarrow V\) (or show that there is no such transformation) for which:Let \(V\) be a vector space with \(\operatorname{dim} V=10\) and let \(L: V \rightarrow V\) be a linear transformation. Consider \(L^{k}: V \rightarro ...
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asked in Mathematics 13 minutes ago
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Let \(L\) be a \(2 \times 2\) matrix. For each of the following give a proof or counterexample.
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Let \(L\) be a \(2 \times 2\) matrix. For each of the following give a proof or counterexample.Let \(L\) be a \(2 \times 2\) matrix. For each of the following give a proof or counterexample. a) If \(L^{2}=0\) then \(L=0\). b) If \(L^{2}=L\) the ...
by MathsGee Platinum
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asked in Mathematics 28 minutes ago
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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 \(W\).
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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 \(W\).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 ...
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asked in Mathematics 30 minutes ago
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Answer the following in terms of \(\mathbf{V}, \mathbf{W}\), and \(\mathbf{Z}\).
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Answer the following in terms of \(\mathbf{V}, \mathbf{W}\), and \(\mathbf{Z}\).Let \(A\) be a matrix, not necessarily square. Say \(\mathbf{V}\) and \(\mathbf{W}\) are particular solutions of the equations \(A \mathbf{V}=\mathbf{ ...
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asked in Mathematics 31 minutes ago
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For each of the following, answer TRUE or FALSE. If the statement is false in even a single instance, then the answer is FALSE.
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For each of the following, answer TRUE or FALSE. If the statement is false in even a single instance, then the answer is FALSE.For each of the following, answer TRUE or FALSE. If the statement is false in even a single instance, then the answer is FALSE. There is no need to ju ...
by MathsGee Platinum
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asked in Mathematics 43 minutes ago
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Let \(V\) be a vector space and \(\ell: V \rightarrow \mathbb{R}\) be a linear map.
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Let \(V\) be a vector space and \(\ell: V \rightarrow \mathbb{R}\) be a linear map.Let \(V\) be a vector space and \(\ell: V \rightarrow \mathbb{R}\) be a linear map. If \(z \in V\) is not in the nullspace of \(\ell\), show that ever ...
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asked in Mathematics 44 minutes ago
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Proof or counterexample. In these \(L\) is a linear map from \(\mathbb{R}^{2}\) to \(\mathbb{R}^{2}\), so its representation will be as a \(2 \times 2\) matrix.

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Let \(A\) be a square matrix with integer elements. For each of the following give a proof or counterexample.
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Let \(A\) be a square matrix with integer elements. For each of the following give a proof or counterexample.Let \(A\) be a square matrix with integer elements. For each of the following give a proof or counterexample. a) If \(\operatorname{det}(A)=\pm 1\), t ...
by MathsGee Platinum
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asked in Mathematics 8 hours ago
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Let \(A: \mathbb{R}^{n} \rightarrow \mathbb{R}^{k}\) be a real matrix, not necessarily square.
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Let \(A: \mathbb{R}^{n} \rightarrow \mathbb{R}^{k}\) be a real matrix, not necessarily square.Let \(A: \mathbb{R}^{n} \rightarrow \mathbb{R}^{k}\) be a real matrix, not necessarily square. a) If two columns of \(A\) are the same, show that \(A ...
by MathsGee Platinum
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asked in Mathematics 9 hours ago
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Let \(A: \mathbb{R}^{n} \rightarrow \mathbb{R}^{k}\) be a real matrix, not necessarily square.
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Let \(A: \mathbb{R}^{n} \rightarrow \mathbb{R}^{k}\) be a real matrix, not necessarily square.Let \(A: \mathbb{R}^{n} \rightarrow \mathbb{R}^{k}\) be a real matrix, not necessarily square. a) If two rows of \(A\) are the same, show that \(A\) ...
by MathsGee Platinum
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asked in Mathematics 9 hours ago
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Let \(A\) be a \(4 \times 4\) matrix with determinant 7 . Give a proof or counterexample for each of the following.
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Let \(A\) be a \(4 \times 4\) matrix with determinant 7 . Give a proof or counterexample for each of the following.Let \(A\) be a \(4 \times 4\) matrix with determinant 7 . Give a proof or counterexample for each of the following.   a) For some vector \(\mat ...
by MathsGee Platinum
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asked in Mathematics 9 hours ago
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Does an 8-dimensional vector space contain linear subspaces \(V_{1}, V_{2}, V_{3}\) with no common non-zero element, such that
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Does an 8-dimensional vector space contain linear subspaces \(V_{1}, V_{2}, V_{3}\) with no common non-zero element, such thatDoes an 8-dimensional vector space contain linear subspaces \(V_{1}, V_{2}, V_{3}\) with no common non-zero element, such that   a). \(\operato ...
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asked in Mathematics 12 hours ago
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What is the logarithmic norm?
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What is the logarithmic norm?What is the logarithmic norm? ...
by Pieter SIlver Status
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asked in Mathematics 1 day ago
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Use Head to Tail Method to represent the following vectors and finally draw Resultant vector.
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Use Head to Tail Method to represent the following vectors and finally draw Resultant vector.F1=12N in the positive x direction.             F2=10N in the positive x direction.  &nbs ...
by Khensanikesty
(104 points)
asked in Physics 2 days ago
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Why is \(|c| ||y|| = ||cy|| \) where \(y\) is a vector and \(c\) is a constant?
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Why is \(|c| ||y|| = ||cy|| \) where \(y\) is a vector and \(c\) is a constant?Why is \(|c| ||y|| = ||cy|| \) where \(y\) is a vector and \(c\) is a constant? ...
by MathsGee Platinum
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asked in Mathematics Jan 15
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What is the dot product of u a row matrix and v a column matrix?
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What is the dot product of u a row matrix and v a column matrix?What is the dot product of u a row matrix and v a column matrix? ...
by MathsGee Platinum
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asked in Mathematics Jan 13
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