Assignment - Homework 4

1. Write the system of equations as a matrix equation AX=B, with A as the coefficient matrix of the system.

x₁ + 3x₂ = - 12

2x₁ +5x₂ = -21

2. Find X₁ and x₂.

3. Use the Gauss-Jordan elimination method to find all solutions of the systems of equations.

3x1 + 2x2 = 16

- 3x₁ + 3x₂ = -6

8x₁ - 23x₂ = -14

4. Perform the indicated operation, if possible.

5. Find the product.

6. Without performing any row operations, explain why the matrix does not have an inverse.

7 Given M, find M¹ and show that M ¹M=I.

8. Find the inverse of the given matrix, if it exists.

9. Write the given system of equations as a matrix equation and solve by using inverses.