Question

solve the following matrix equation for the matrix a. enter all answers in exact, reduced form. no decimals are allowed. any negative signs must be in the numerator. −3A − 7[-6] =9A −6 [0] [3] [5] A =

Answer 1

Step 1:
Start by writing out the given matrix equation.

-3A - 7[-6]
[ 0] = 9A - 6[3]
[ 5]

Step 2:
Move terms involving A to one side of the equation and constants to the other side.

-3A - 9A = -7[-6] -6[3]
[ 5]

Combine like terms to get
-12A = -42 - 6[3]
[ 5]

Thus,
-12A = -42 - 18
[ 30]

Step 3:
Collect like terms by adding 42 and 18 to each side of the equation:

-12A = -24
[ 12]

To isolate A, divide each side of the equation by -12 (the coefficient of A):

A = 24 / -12
[ -12 / -12]

Step 4:
Reduce the fractions:

A= -2
[ -1]

Thus, the solution of the matrix equation for A is:

Matrix A =
[ -2 ]
[ -1 ]

Please note that in matrix algebra, the division operation is performed element-wise. Hence, each element of the matrix -24 / -12 results in the matrix A as shown above.