Question

Let A and B be 6×6 matrices such that det(A)= 3 and det(B)=2

What is det(−2A^{T}?^{-1})? Justify your
answer.

Answer #1

Let A and B be 3x3 matrices with det(A) = 2 and det(B) = -3.
Find
a. det(AB) show all steps.
b. det(2B) show all steps.
c. det(AB^-1) show all steps.
d. det(2AB) show all steps.

If A, B, and C are 4x4 matrices; and det(A) = 1, det(B) = -5,
and det(C) = -3, then compute:
det(4B3A-1C-1A-1B2)
= ____

Suppose A, B, C are n x n matrices with det. A =1,det
B =-1, det C is 2, find AB, A+B,

If I prove Det(A)Det(B) = Det(AB) for matrices A and B when A
and B are 2x2 matrices, can I use that to show that Det(A)Det(B) =
Det(AB) for any n x n matrix? If so how?

Let A,B,C be 4x4 matrices.If det(A)=12,det(B)=48 and det(C)=-3,
then what is det(3AB-2C-3)

Let A and B be 3x3 matricies, with det A = 9 and deb B = 6. Use
properties of determinants to complete the parts below.
1. Compute det AB
2. Compute det 5A
3. Compute det Bt
4. Compute det A-1
5. Compute det A3

True or False
1.) det(A-B) = det(A) - det(B)
2.) det(cA) = c*det(A)
3.)det(ABT)=det(ATB)
4.)det(A-B)=0 implies A=B

In what follows, A and B denote 2 x 2 matrices. Answer each
question below, with justification. No one answer should be more
than a few lines long.
A1. If k is a scalar, how does the determinant of
kA relate to the determinant of A?
A2. Show that the determinant of A + B is not necessarily the
same as det A + det B. (Remark: a single specific counterexample
suffices!)
A3. If A is singular and B is...

Let A, B, and C be n×n matrices of the form A= [c_1...x...c_n],
B= [c_1...y...c_n], and C= [c_1...x+y...c_n] where x, y, and x+y
are the jth column vectors. Use cofactor expansions to prove that
det(C)=det(A)+det(B).

Let V be the vector space of 2 × 2 matrices over R, let <A,
B>= tr(ABT ) be an inner product on V , and let U ⊆ V
be the subspace of symmetric 2 × 2 matrices. Compute the orthogonal
projection of the matrix A = (1 2
3 4)
on U, and compute the minimal distance between A and an element
of U.
Hint: Use the basis 1 0 0 0
0 0 0 1
0 1...

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