Matrix Equations Worksheet

Solutions

1Given the matrices:

Matrices

Solve the matrix equation:

A · X = B

2Given the matrices:

Matrices

Solve the matrix equation:

X · A + B = C

3Given the matrices:

Matrices

Solve the matrix equations:

Matrix Equations

Matrix Equations

Matrix Equations

Matrix Equations

Matrix Equations

4Given the matrices:

Matrices

Solve the matrix equation:

A X + 2 B = 3 C

5Solve the matrix equation:

A · X + 2 · B = 3 · C

Matrices

6Solve the system using a matrix equation.

System of Equations

7Calculate A and B:

System of Equations

8Solve the following equations without developing the determinants.

1 Matrix Equation

2 Matrix Equation


1

1Given the matrices:

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

Matrix Equation Operations

Matrix Equation Operations


2

Given the matrices:

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

Matrix

Matrix Equation Operations

Matrix Equation Solution


3

Given the matrices:

Matrices

Solve the matrix equations:

Matrix Equation

Matrix Equation Operations

Matrix Equation Operations

Matrix Equation Operations

Matrix Equation Solution


Matrix Equation

Matrix Equation Operations

Matrix Equation Operations

Matrix Equation Operations

Matrix Equation Operations

Matrix Equation Solution


Matrix Equation

Matrix Equation Operations

Matrix Equation Operations

Matrix Equation Operations

Matrix Equation Solution


Matrix Equation

Matrix Equation Operations

Matrix Equation Operations

Matrix Equation Operations

Matrix Equation Operations

Matrix Equation Solution


Matrix Equation

Matrix Equation Operations

Matrix Equation Operations

Matrix Equation Operations

Matrix Equation Operations

Matrix Equation Solution


4

Given the matrices:

Matrices

Solve the matrix equation:

Matrix Equation Operations

Matrix Equation Operations

Matrix Equation Operations

Matrix Equation Operations

Matrix Equation Operations

Matrix Equation Operations

Matrix Equation Operations

Matrix Equation Operations

Matrix Equation Operations

Matrix Equation Solution


5

Solve the matrix equation:

A · X + 2 · B = 3 · C

Matrices

|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)

Matrix Equation Operations

Matrix Equation Operations

Matrix Equation Solution


6

Solve the system using a matrix equation.

System of Equations

Matrix Equation Operations

Matrix Equation Operations

Matrix Equation Operations

Matrix Equation Operations

Matrix Equation Operations

Matrix Equation Operations

Matrix Equation Operations

Matrix Equation Operations


7

Calculate A and B:

System of Equations

Multiply the second equation by −2.

Matrix Equation Operations

Add the equations.

Matrix Equation Operations

Multiply the first equation by 3 and add the equations:

Matrix Equation Operations


8

Solve the following equations without developing the determinants.

1 Matrix Equation

Matrix Equation Operations

2 Matrix Equation

Matrix Equation Operations

Matrix Equation Operations