LearningCat

19 Questions
3 Answers

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precalc help

Given a square matrix $\mathbf{A}$, the characteristic polynomial of $\mathbf{A}$ is defined as \[P_{\mathbf A}(t) = \det (t \mathbf{I} - \mathbf{A}),\]
where $\mathbf{I}$ is the identity matrix. For example, read more ..

LearningCat Jun 11, 2024

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21

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Precalc

Let the vectors i and j be defined as usual:
\[\mathbf{i} = \begin{pmatrix} 1 \\ 0 \end{pmatrix}, \mathbf{j} = \begin{pmatrix} 0 \\ 1 \end{pmatrix}.\]
Let A be a matrix such that Ai, Aj match the picture below:
read more ..

LearningCat May 31, 2024

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Precalc

Find all 2 x 2 matrices A that have the property that for any 2 x 2 matrix B, \[\mathbf{A} \mathbf{B} = \mathbf{B} \mathbf{A}.\]

LearningCat May 31, 2024

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21

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Precalc question

Let A and B be the following matrices:
A rotates vectors by $\frac{\pi}{4}$ counterclockwise,
B is matrix \begin{pmatrix} 1 & 1 \\ 0 & 1 \end{pmatrix}.
Calculate \[\mathbf{A}^{102} \mathbf{B}^{102} - \mathbf{B}^{102} \mathbf{A}^{102} read more ..

LearningCat May 31, 2024

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Let matrix A and the vectors v_1 and v_2 be defined below: A= \begin{bmatrix} -1 && -6 \\ 2 && -6 \end{bmatrix}

Let matrix A and the vectors v_1 and v_2 be defined below: A=\begin{bmatrix} -1 && -6 \\ 2 && -6 \end{bmatrix}, v_1=(2;-1) and v_2=(3;-2).
Show that A sends vectors v_1 and v_2 to scalar multiples of themselves read more ..

LearningCat May 21, 2024

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20

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Preclac

Let x and y be two perpendicular unit vectors.
(a) Find a formula for the magnitude of an arbitrary linear combination ax+by
of x and y in terms of a and b.
(b) Find the precise condition on a,b,c and d under which the linear combinations read more ..

LearningCat May 14, 2024

+68

0

Could you show me how you got that?

LearningCatMay 14, 2024

+68

+1

How did you get a = ( 0, m) and b = (m , 0). Why the 0?

LearningCatMay 7, 2024