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Determine whether the matrix is invertible. 75 -7 42 -4 -30 3 O No YesCompute the determinant of the matrix by cofactor expansion. 4 2 3 1 3 5 3 5 4 O A. 42 O B. - 42 O C. - 102 O D. 228Find the inverse of the matrix A, if it exists. 4 - 2 8 A= 4 - 1 8 3 -3 16 . . . O A. A does not exist. O B. 102 A= 0 10 0 0 0 O C. 4 4 8 OD. 1 02 A - 1 = -2 -1 -3 A-1= 0 10 8 3 16 0 NW 0Explore the effects of an elementary row operation on the determinant of a matrix. State the row operation and describe how it affects the determinant. -5 9 -5 -5 9 -5 1 1 1 , k k k 3 -2 2 3 -2 2 What is the elementary row operation? 0 A. Replace row 2 with k times row 2. O B. Replace row 2 with row 2 divided by k. 0 C. Replace row 2 with k plus row 2. O D. Replace row 2 with row 2 minus k. How does the row operation aect the determinant? O A. The determinant is decreased by 3k. 0 B. The determinant is increased by 3k. 0 C. The determinant is multiplied by k. 0 D. The determinant does not change. 1 - 2 3 Let T be the linear transformation whose standard matrix is A = - 1 3 - 4 . Determine whether the linear transformation T is one-to-one and whether it maps R onto R3. 3 - 3 3 . . . O A. T is not one-to-one and does not map R onto R 3. O B. T is one-to-one, but does not map R onto R 3. O C. T is not one-to-one, but maps R' onto R 3. O D. T is one-to-one and maps R onto R 3