Question

B is a matrix (3 2)and C is the matrix (9 -3)
(2 2). (2 1)
Of a matrix is a 2×2 matrix and A×B=C determine matrix of A

Answer 1

To determine the matrix A, we can use the equation A x B = C and solve for A.

Let's represent the elements of matrix A as follows:

A = | a b |
| c d |

Using matrix multiplication, the equation A x B = C becomes:

| 3 2 | | a b | = | 9 -3 |
| c d | | 2 1 |

Multiplying the matrices on the left side, we have:

| 3a + 2c 3b + 2d | = | 9 -3 |
| 2 1 |

From this equation, we can equate the corresponding elements:

3a + 2c = 9,
3b + 2d = -3,
a + c = 2,
b + d = 1.

From the first equation, we can solve for a:

3a = 9 - 2c,
a = (9 - 2c)/3.

Similarly, from the third equation, we can solve for c:

c = 2 - a.

Substituting the value of c into the first equation, we have:

3a = 9 - 2(2 - a),
3a = 9 - 4 + 2a,
a - 2a = 5,
-a = 5,
a = -5.

Substituting the value of a back into c = 2 - a:

c = 2 - (-5),
c = 7.

Now that we have found the values of a and c, we can solve for b and d using the second and fourth equations:

3b + 2d = -3,
b + d = 1.

From the fourth equation, we have:

b = 1 - d.

Substituting this value of b into the second equation, we have:

3(1 - d) + 2d = -3,
3 - 3d + 2d = -3,
-d = -6,
d = 6.

substituting the value of d back into b = 1 - d:

b = 1 - 6,
b = -5.

Therefore, the matrix A is:

A = | -5 -5 |
| 7 6 |