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7 1 4 1 5) (a) (7 points) Find the determinant of the matrix 1 0 7 0 .
0362
(b) (8 points) Assume that A, B , and C are invertible 3 × 3 matrices, det A = a, det B =
b, and det C = c where c = 0. Find, with explanation, det(A3 ), det(5A), det(C T ) and
det(AT B 2 C −1 ). x + a x + 2a x + 3a
(c) (6 points) In terms of x and a, ﬁnd the determinant of x + 2a x + 3a x + 4a .
x + 4a x + 5a x + 6a
a
b Solution: (a) Using the cofactor method along the top row will reduce this determinant
problem to simply taking the determinant of two 3 × 3 matrices and adding them. Then, we expand along the rows of the cofactors that only have a s...
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 Fall '05
 HUI
 Linear Algebra, Algebra, Vectors

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