Matrix Equations Worksheet

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.

Add the equations.

Multiply the first equation by 3 and add the equations:

8

Solve the following equations without developing the determinants.

1

2