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4) Determine if each matrix below is invertible, use the Invertible Matrix Theorem to explain your conclusion: Ifa matrix is invertible, find the inverse

[-2 A =

~6

~1 -2

10 3 -3

c = [-6 -3 -2

B = [4 31 ~2 10]

D =

5) Determine if each set of vectors is a basis for the given space

{l3 -3 5

for R3

{1H [-:1 , [-21} for R2

2 3

1 3

4

LLL

for R3

{[I4 [421} for R2

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02:51

Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer:-5Choose the correct answer below:0A The matrix is invertible. The columns of the given matrix span are linearly dependent: 0 B. The matrix is not invertible. If the given matrix is A, the equation Ax = b has a solution for at least one b in R3 . 0c. The matrix is not invertible. If the given matrix is A, A is not row equivalent to the nxn identity matrix 0 D: The matrix is invertible. The given matrix has 3 pivot positions

04:55

1. Use the fact thatmatrices A and B arerow-equivalent.A = −2−580−1713−515311−197117−135−3B = 1010101−2030001−500000(a) Find the rank and nullity of A.(b) Find a basis for the nullspace of A.(c) Find a basis for the row space of A.(d) Find a basis for the column space of A.

04:28

Assume that the matrix A is row equivalent to B. Find a basis for the row space of the matrix A-29{(1,3,-4,0,1), (2,4,-5,2),-5,(1,45,0,.3,21, (-3,+1,8,3, {(1,3,-4,0, 1), (0,-2,3,2,-71, (0,0, 8,-11,29)} {(1, 0,0,0), (3,-2, 0,01, (-4,3,-8,0)} {(1,3,-4,0,1), (0,-2,3,2,.7), (0, 0,-8,-11,29), (0, 0,0,0,0)}

04:38

Suppose B and D are both invertible matrices, and A is the block matrixA =5| Show that 4 is invertible; and its inverse isB^-1 ~ B^-1CD^-1 A^-1 = 0 D^-1

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