Question

What are the determinants for solving this linear system? 5x + 3y = 17 −8x − 3y = 9 |A| = |Ax| = |Ay| =

Answer 1

|A| = | 5, 3, -8, -3 |

|A ₓ| = | 17, 3, 9, -3 |

|Aᵧ| = | 5, 17, -8, 9 |

Answer 2

For this case we have the following system of equations:

`image`

We can Rewrite the system of equations of the form:

`image`

Where,

A: coefficient matrix

x: incognita vector

b: vector solution

We have then:

`A=\left[\begin{array}{ccc}5&3\\-8&-3\end{array}\right]`

`x=\left[\begin{array}{ccc}x\\y\end{array}\right]`

`b=\left[\begin{array}{ccc}17\\9\end{array}\right]`

Then, the determinant of matrix A is given by:

`image`

`|A|=-15+24`

`|A|=9`

Answer:

The determinants for solving this linear system are:

`|A|=9`