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Let \(U, V, W\) be orthogonal vectors and let \(Z=a U+b V+c W\), where \(a, b, c\) are scalars.
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Let \(U, V, W\) be orthogonal vectors and let \(Z=a U+b V+c W\), where \(a, b, c\) are scalars.Let \(U, V, W\) be orthogonal vectors and let \(Z=a U+b V+c W\), where \(a, b, c\) are scalars. a) (Pythagoras) Show that \(\|Z\|^{2}=a^{2}\|U\|^{2}+b ...
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asked in Mathematics Jan 21
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Let \(V, W\) be vectors in \(\mathbb{R}^{n}\).
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Let \(V, W\) be vectors in \(\mathbb{R}^{n}\).Let \(V, W\) be vectors in \(\mathbb{R}^{n}\). a) Show that the Pythagorean relation \(\|V+W\|^{2}=\|V\|^{2}+\|W\|^{2}\) holds if and only if \(V\) a ...
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asked in Mathematics Jan 21
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Let \(\mathcal{P}_{2}\) be the space of polynomials of degree at most 2 .
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Let \(\mathcal{P}_{2}\) be the space of polynomials of degree at most 2 .Let \(\mathcal{P}_{2}\) be the space of polynomials of degree at most 2 .   a) Find a basis for this space. b) Let \(D: \mathcal{P}_{2} \righta ...
by MathsGee Platinum
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asked in Mathematics Jan 21
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If \(A\) and \(B\) are \(4 \times 4\) matrices such that \(\operatorname{rank}(A B)=3\), then \(\operatorname{rank}(B A)<4\).
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If \(A\) and \(B\) are \(4 \times 4\) matrices such that \(\operatorname{rank}(A B)=3\), then \(\operatorname{rank}(B A)<4\).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 ...
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asked in Mathematics Jan 21
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Let \(A: \mathbb{R}^{n} \rightarrow \mathbb{R}^{k}\) be a linear map. Show that the following are equivalent.
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Let \(A: \mathbb{R}^{n} \rightarrow \mathbb{R}^{k}\) be a linear map. Show that the following are equivalent.Let \(A: \mathbb{R}^{n} \rightarrow \mathbb{R}^{k}\) be a linear map. Show that the following are equivalent. a) For every \(y \in \mathbb{R}^{k}\) th ...
by MathsGee Platinum
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asked in Mathematics Jan 20
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What are the rules of differentiation?
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What are the rules of differentiation?What are the rules of differentiation? ...
by MathsGee Platinum
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asked in Mathematics Jan 15
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Verify that the Cauchy-Schwarz inequality holds. \(\mathbf{u}=(0,2,2,1), \mathbf{v}=(1,1,1,1)\)
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What is the dot product of $\mathbf{u}$ a column matrix and $\mathbf{v}$ a column matrix?
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What is the dot product of $\mathbf{u}$ a column matrix and $\mathbf{v}$ a column matrix?What is the dot product of $\mathbf{u}$ a column matrix and $\mathbf{v}$ a column matrix? ...
by MathsGee Platinum
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asked in Mathematics Jan 13
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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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What is the dot product of u a column matrix and v a row matrix?
1 answer 13 views
What is the dot product of u a column matrix and v a row matrix?What is the dot product of u a column matrix and v a row matrix? ...
by MathsGee Platinum
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asked in Mathematics Jan 13
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Verify that the Cauchy–Schwarz inequality holds for $\mathbf{u}=(0,2,2,1), \mathbf{v}=(1,1,1,1)$
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Verify that the Cauchy–Schwarz inequality holds for $\mathbf{u}=(4,1,1), \mathbf{v}=(1,2,3)$
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Verify that the Cauchy–Schwarz inequality holds for $\mathbf{u}=(1,2,1,2,3), \mathbf{v}=(0,1,1,5,-2)$
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Show that two nonzero vectors $\mathbf{v}_{1}$ and $\mathbf{v}_{2}$ in $R^{3}$ are orthogonal if and only if their direction cosines satisfy
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When are two nonzero vectors orthogonal to each other?
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When are two nonzero vectors orthogonal to each other?When are two nonzero vectors orthogonal to each other? ...
by MathsGee Platinum
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asked in Mathematics Jan 13
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