LearningCat

19 Questions
3 Answers

0

29

1

+68

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, mehr ..

LearningCat 11.06.2024

0

31

1

+68

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:
mehr ..

LearningCat 31.05.2024

0

40

1

+68

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 31.05.2024

0

45

1

+68

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} mehr ..

LearningCat 31.05.2024

0

23

1

+68

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 mehr ..

LearningCat 21.05.2024

0

40

1

+68

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 mehr ..

LearningCat 14.05.2024

+68

0

Could you show me how you got that?

LearningCat14.05.2024

+68

+1

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

LearningCat07.05.2024