Questions:
1. Write the matrix equation as a system of equations and solve the system.
1 2 3 { x { 1
1 1 1 { y = { 12
-1 1 2 { z { 2
2. Find the determinant of the given matrix.
1 0 6 -1
-6 0 2 4
3 0 6 -2
3 4 -3 3
3. Find the determinant of the given matrix.
-1 2 -2
5 -1 -5
5 4 4
4. Determine whether the matrix is invertible by finding the determinant of the matrix.
[1/6 -1/7]
[ -49 42]
5. Find the inverse of the matrix.
A = 3 0
-1 -4
6. Perform the indicated operation, if possible.
[-1 0] - [-1 4]
[4 3] [ 3 1]
7. Decide whether or not matrix B is the inverse of matrix A.
A = [-5 1]
[-7 1]
B = [ 1/2 -1/2]
[ 7/2 -5/2]
8. The size of two matrices is given. Find the size of the product AB and the product BA, if the products exist.
A is 4 x 1, B is 1 x 4
9. Given matrices A and B, find the indicated matrix if possible.
A = [-2 0] B = [-3 ] Find AB.
[ 1 -5 ] [ 2 ]
10. Write the augmented matrix for the system.
9x + 2y + 9z = 8
8x + 5y + 2z = 26
9x + 2y + 3z + 14
11. Find the sum, if possible.
8 8 3 -4
-3 3 + -7 -5
4 3 5 8
12. Find the minor for the element in the first row and second column of the given matrix.
11 -11 20
-3 19 16
4 6 -8