# Matrix Equations Worksheet

### Solutions

1Given the matrices:

Solve the matrix equation:

A · X = B

2Given the matrices:

Solve the matrix equation:

X · A + B = C

3Given the matrices:

Solve the matrix equations:

4Given the matrices:

Solve the matrix equation:

A X + 2 B = 3 C

5Solve the matrix equation:

A · X + 2 · B = 3 · C

6Solve the system using a matrix equation.

7Calculate A and B:

8Solve the following equations without developing the determinants.

1

2

## 1

1Given the matrices:

Solve the matrix equation:

A · X = B

|A|=1 ≠ 0, there is the inverse A−1.

A−1 (A · X) = A−1 · B

(A−1 · A) · X = A−1 · B

I · X = A−1 · B

X = A−1 · B

## 2

Given the matrices:

Solve the matrix equation:

X · A + B = C

|A| = 1 ≠ 0

(X · A + B) − B = C B

X · A + (B B) = C B

X · A + 0 = C B

X · A = C B

X · A · A−1 = (C B) · A−1

X (A · A−1 ) = (C B) · A−1

X · I = (C B) · A−1

X = (C B) · A−1

## 3

Given the matrices:

Solve the matrix equations:

## 4

Given the matrices:

Solve the matrix equation:

## 5

Solve the matrix equation:

A · X + 2 · B = 3 · C

|A| = 1 ≠ 0

(A · X +2 · B) − 2 · B = 3 · C − 2B

A · X + ( 2 · B − 2 · B) = 3 · C − 2B

A · X + 0= 3 · C − 2B

A· X = 3 · C − 2B

(A−1 · A) · X = A−1 · (3 · C − 2B)

I · X = A−1 · (3 · C − 2B)

X = A−1 · (3 · C − 2B)

## 6

Solve the system using a matrix equation.

## 7

Calculate A and B:

Multiply the second equation by −2.