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LearningCat
Score
68
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Questions
16
Answers
3
19 Questions
3 Answers
0
9
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,
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LearningCat
Jun 11, 2024
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11
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:
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LearningCat
May 31, 2024
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7
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+68
Precalc
Find all 2 x 2 matrices A that have the property that for any 2 x 2 matrix B, \[\mathbf{A} \mathbf{B} = \mathbf{B} \mathbf{A}.\]
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LearningCat
May 31, 2024
0
11
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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}
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LearningCat
May 31, 2024
0
5
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
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LearningCat
May 21, 2024
0
12
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
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LearningCat
May 14, 2024
0
18
2
+68
Precalculus
Help please :3
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LearningCat
May 14, 2024
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5
2
+68
Precalculus help
Then what is vector AB? Help :3
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LearningCat
May 14, 2024
0
6
1
+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
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MaxWong
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LearningCat
May 14, 2024
0
5
3
+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
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LearningCat
May 7, 2024
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26
1
+68
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).
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LearningCat
Feb 27, 2024
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32
1
+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
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LearningCat
Feb 13, 2024
+1
4
3
+68
Trig question
For how many values of such that do we have ? (Note that is a measure in radians, not degrees!)
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LearningCat
Feb 6, 2024
0
36
1
+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.
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LearningCat
Oct 31, 2023
0
40
1
+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.
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LearningCat
Oct 28, 2023
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31
1
+68
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
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LearningCat
Oct 28, 2023
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#2
+68
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Could you show me how you got that?
LearningCat
May 14, 2024
#2
+68
+1
How did you get a = ( 0, m) and b = (m , 0). Why the 0?
LearningCat
May 7, 2024