Question

Can someone please help me on this pre calculous question? We need a calculator to solve I think

We need to find the inverse of the matrix

Answer 1

`\[ A^(-1) \approx \begin{bmatrix} 0.139051 & -0.037482 \\ -2.086455 & 0.093153 \end{bmatrix} \]`

Given matrix
`\(A\)`:

`\[ A = \begin{bmatrix} (4)/(3) & 0.8 \\ 26 & √(3) \end{bmatrix} \]`

Calculate the determinant (\(ad - bc\)):

`\[ \text{Determinant} = \left((4)/(3) \cdot √(3)\right) - (0.8 \cdot 26) \]`

`\[ \text{Determinant} = (4√(3))/(3) - 20.8 \]`

Now, calculate the inverse matrix components:

`\[ A^(-1) = \frac{1}{\text{Determinant}} \begin{bmatrix} √(3) & -0.8 \\ -26 & (4)/(3) \end{bmatrix} \]`

`\[ A^(-1) = (1)/((4√(3))/(3) - 20.8) \begin{bmatrix} √(3) & -0.8 \\ -26 & (4)/(3) \end{bmatrix} \]`

Substitute the calculated determinant value and perform the arithmetic:

`\[ A^(-1) = (1)/(\left((4√(3))/(3) - 20.8\right)) \begin{bmatrix} √(3) & -0.8 \\ -26 & (4)/(3) \end{bmatrix} \]`

Now, find the inverse matrix values and round each entry to six decimal places.

`\[ A^(-1) \approx \begin{bmatrix} 0.139051 & -0.037482 \\ -2.086455 & 0.093153 \end{bmatrix} \]`

Therefore, the rounded inverse matrix \(A^{-1}\) is:

`\[ A^(-1) \approx \begin{bmatrix} 0.139051 & -0.037482 \\ -2.086455 & 0.093153 \end{bmatrix} \]`