Using matrix to solve linear system of equations

Question

Questions:

Using matrix to solve linear system of equations

1. Find the equation of the line shown:

  

2. A bank loaned $15,000, some at an annual rate of 16% and some at an annual rate of 10%. If the income from these loans was $1800, how much was loaned at 10%?

3. Write the augmented matrix of the system: (see attachment).

                 2x₁ -3x₂ + x₃ = 0     x₁ - x₂ - 2x₃ = -2      -5x₁ + x₂ = -4

4. Perform the row operation R2 = (-2)r₁ + r₂ on the matrix.

                   | 1   5   -6  |                     
                   | 6   -1   2  |               

5. Indicate whether the reduced row-echelon form of each augmented matrix has one solution, no solution, or infinitely solutions.

A. | 1  0  0| 1 |
    | 0  1  0| 2 |                 
    | 0  0  0| 0 |

B. | 1  0  0| 1 |
    | 0  1  0| 2 |                 
    | 0  0  1|-1 |

C  | 1  0  0 |3|
    | 0  1  0| 2|                 
    | 0  0  0| 1|

6. Find : 2 | 1   0 |   | 8    2 |
                 | 3   2 | - |-1   0 |
                 |-1   1 |   | 1    1|

7. Find: | 4   3 | x | 1   0    2 |
             | 0   1 |    | 2  -1    0 |

8. Find inverse of : | 1   2   1 |
                              | 1   1   2 |
                              | 2   0   2 |