# Worksheet: Finding an Unknown Matrix

In this worksheet, we will practice using operations on matrices and matrix inversion to find an unknown matrix as an introduction to solve a system of linear equations.

**Q1: **

Consider the matrices Find the matrix that satisfies the equation .

- A
- B
- C
- D

**Q2: **

Given that what are and ?

- A ,
- B ,
- C ,
- D ,

**Q3: **

Adam guesses that any matrix , where , must be a combination of and . In other words, it must be for some numbers and . Ramy wants to challenge this, since he see that produces the same product when multiplied on either side. Help Adam by finding and so that

- A
- B
- C
- D
- E

**Q4: **

Given that find the values of and that satisfy , where is the zero matrix of order and is the unit matrix of order .

- A ,
- B ,
- C ,
- D ,

**Q5: **

Given that find the values of and .

- A ,
- B ,
- C ,
- D ,

**Q6: **

Given that find the matrix .

- A
- B
- C
- D

**Q7: **

Given that find the matrix .

- A
- B
- C
- D

**Q8: **

Determine , given that

- A
- B
- C
- D

**Q9: **

Solve the matrix equation .

- A
- B
- C
- D
- E

**Q10: **

Find the matrix that satisfies the equation .

- A
- B
- C
- D

**Q11: **

Given that

solve the following matrix equation for :

- A
- B
- C
- D
- E

**Q12: **

Given that find the matrix .

- A
- B
- C
- D
- E

**Q13: **

Given that solve the equation

- A
- B
- C
- D

**Q14: **

Consider the matrices Determine the matrix that satisfies .

- A
- B
- C
- D

**Q15: **

Consider the matrices and : Find .

- A
- B
- C
- D

**Q16: **

Given that determine the matrix that satisfies the relation .

- A
- B
- C
- D

**Q17: **

Let and . Solve the matrix equation for the matrix .

- A
- B
- C
- D
- E

**Q18: **

Consider the matrices Find the matrix that satisfies the equation .

- A
- B
- C
- D

**Q19: **

Consider the matrices Find the matrix that satisfies the equation .

- A
- B
- C
- D

**Q20: **

Given that what are and ?

- A ,
- B ,
- C ,
- D ,