6) Use this list of properties to help save you lots of calculations as you answer...

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6) Use this list of properties to help save you lots of calculations as you answer the questions below. Properties of Determinants: (a) The determinant of any size identity matrix is 1. (b) The determinant changes sign when two rows are exchanged. (c) If two rows of A are equal, then det(A) = 0. (d) A matrix with a row of zeros has det(A) = 0. (e) Subtracting a multiple of one row from another row leaves det(A) unchanged. (f) If A is triangular then det(A) is the product of the diagonal entries. (g) The determinant of AB is det(A) times det(B). Thus, |AB| = |A||B| (h) The transpose AT has the same determinant as A. (i) The determinant of A-1 (j) If A is an n x n matrix then det(kA) = k"det(A). (k) det(AP) = [det(A)]P (a) Let A = Find det(A) (b) Find the inverse of A. Call it B = A-1. (c) Find det(B). (d) Find det(6A). (e) Find det(BA*B") 49 1 0 -2 2 10 0 4 -9 0 0 (f) Let C = Find det(C). 1 6) Use this list of properties to help save you lots of calculations as you answer the questions below. Properties of Determinants: (a) The determinant of any size identity matrix is 1. (b) The determinant changes sign when two rows are exchanged. (c) If two rows of A are equal, then det(A) = 0. (d) A matrix with a row of zeros has det(A) = 0. (e) Subtracting a multiple of one row from another row leaves det(A) unchanged. (f) If A is triangular then det(A) is the product of the diagonal entries. (g) The determinant of AB is det(A) times det(B). Thus, |AB| = |A||B| (h) The transpose AT has the same determinant as A. (i) The determinant of A-1 (j) If A is an n x n matrix then det(kA) = k"det(A). (k) det(AP) = [det(A)]P (a) Let A = Find det(A) (b) Find the inverse of A. Call it B = A-1. (c) Find det(B). (d) Find det(6A). (e) Find det(BA*B") 49 1 0 -2 2 10 0 4 -9 0 0 (f) Let C = Find det(C). 1

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AMuer 6 A 3 1 2 det A 3x2 4 x1 2 B A 6 3D Adj A I2 ... View the full answer