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

0

6

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+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:
read more ..

LearningCat May 31, 2024

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5

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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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8

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+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} read more ..

LearningCat May 31, 2024

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4

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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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9

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+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 read more ..

LearningCat May 14, 2024

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Precalculus

LearningCat May 14, 2024

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Precalculus help

Then what is vector AB? Help :3

LearningCat May 14, 2024

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+68

Precalc help

Let u and v be vectors such that ||u||=3 and ||v||=2 such that the angle between u and v when placed tail to tail is 60 degrees.
Let A be a matrix such that row_1(A)=u and row_2(A)=v.
Then what are Au, Av in that order? (Your answers read more ..

LearningCat May 14, 2024

0

4

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+68

Precalc

Let a and b be two vectors such that neither of a-b and a+b is the zero vector.
(a) Prove that if the vectors a and b are of equal length, then a-b and a+b are perpendicular.
(b) Prove that if a-b and a+b are perpendicular, then a and b are read more ..

LearningCat May 7, 2024

-1

22

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Trig help

Find constants a, b, c, d and e such that cos4x=a(sin^4)x+b(sin^3)x+c(sin^2)x+d(sin)x+e for all angles x. In other words, write cos(4x) as a polynomial in sin(x).

LearningCat Feb 27, 2024

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23

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+68

Trig question help

Point is the terminal point of angle theta. Points Q, R, and S and are other terminal points.

List the points P,Q,R, and S and in read more ..

LearningCat Feb 13, 2024

+1

4

3

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Trig question

For how many values of such that do we have ? (Note that is a measure in radians, not degrees!)

LearningCat Feb 6, 2024

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30

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+68

help :3

In square ABCD, P is on BC such that BP=4 and PC=1, and Q is on CD such that DQ=4 and QC=1. Find sin of angle PAQ.

LearningCat Oct 31, 2023

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32

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+68

Geometry :3

In traingle ABC, point X is on side BC such that AX=13, BX=10, and CX=4, and the circumcircles of triangles ABX and ACX have the same radius. Find the area of triangle ABC.

LearningCat Oct 28, 2023

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30

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geometry problem halp :3

Let R be the circle centered at (0,0) with radius 10. The lines x=6 and y=4 divide R into four regions R1, R2, R3 , and R4. Let R_i denote the area of region R_i If R1>R2>R3>R4,
then find R1-R2-R read more ..

LearningCat Oct 28, 2023

+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