Vaz_MAT_343_ONLINE_B_Fall_2019.hourogne.Section_2.2_Properties_of_Determinants (1).pdf - Hassan Ouro-gneni Vaz MAT 343 ONLINE B Fall 2019 Assignment

# Vaz_MAT_343_ONLINE_B_Fall_2019.hourogne.Section_2.2_Properties_of_Determinants (1).pdf

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Hassan Ouro-gneni Vaz MAT 343 ONLINE B Fall 2019 Assignment Section 2.2 Properties of Determinants due 10/26/2019 at 11:59pm MST 1. (1 point) If A and B are 3 × 3 matrices, det ( A ) = - 5, det ( B ) = - 3, then det ( AB ) = , det ( - 2 A ) = , det ( A T ) = , det ( B - 1 ) = , det ( B 2 ) = . Solution: det ( AB ) = det ( A ) det ( B ) = - 5 ( - 3 ) = 15 Every time we multiply a row by a scalar, the determinant is multiplied by that scalar. The matrix A has 3 rows, thus det ( - 2 A ) = ( - 2 ) 3 det ( A ) = ( - 2 ) 3 ·- 5 det ( A T ) = det ( A ) = - 5 det ( B - 1 ) = 1 det ( B ) = 1 - 3 det ( B 2 ) = det ( B ) 2 = ( - 3 ) 2 Answer(s) submitted: 15 40 -5 -1/3 9 (correct) Correct Answers: 15 40 -5 -0.333333333333333 9 2. (1 point) If the determinant of a 3 × 3 matrix A is det ( A ) = 3, and the matrix B is obtained from A by multiplying the second row by 4, then det ( B ) = . Solution: By properties of determinants, if a row (or col- umn) of a matrix is multiplied by a scalar, the determinant is multiplied by the same scalar. Thus det ( B ) = 4 · det ( A ) = 4 ( 3 ) = 12 Answer(s) submitted: 12 (correct) Correct Answers: 12 3. (1 point) If the determinant of a 5 × 5 matrix A is det ( A ) = 8, and the matrix C is obtained from A by swapping the first and fourth rows, then det ( C ) = . Solution: By properties of determinants, if two rows are switched, the determiants changes sign. Thus det ( B ) = - det ( A ) = - 8 Answer(s) submitted: -8 (correct) Correct Answers: -8 4. (1 point) If the determinant of a 4 × 4 matrix A is det ( A ) = 8, and the

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