Consider this matrix: [[10,0],[-8,1]] Find the inverse of the matrix. Give exact values. Non-integers can be given as decimals or as simplified fractions.

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Consider this matrix:  [[10,0],[-8,1]] Find the inverse of the matrix. Give exact values. Non-integers can be given as decimals or as simplified fractions.

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Calculate Determinant: To find the inverse of a 2x2 matrix, we use the formula: $$ A^{-1} = \frac{1}{\text{det}(A)} \begin{bmatrix} d & -b \ -c & a \end{bmatrix} $$ where $ A = \begin{bmatrix} a & b \ c & d \end{bmatrix} $ and $\text{det}(A) = ad - bc$. For the given matrix $ A = \begin{bmatrix} 10 & 0 \ -8 & 1 \end{bmatrix} $, we have $ a = 10 $, $ b = 0 $, $ c = -8 $, and $ d = 1 $. First, we calculate the determinant of $ A $: $\text{det}(A) = (10)(1) - (0)(-8) = 10 - 0 = 10$.Apply Inverse Formula: Now that we have the determinant, we can find the inverse by applying the formula: $$ A^{-1} = \frac{1}{10} \begin{bmatrix} 1 & -0 \ 8 & 10 \end{bmatrix} $$ Simplify the matrix by multiplying each element by $ \frac{1}{10} $: $$ A^{-1} = \begin{bmatrix} \frac{1}{10} & 0 \ \frac{8}{10} & 1 \end{bmatrix} $$ Further simplification gives us: $$ A^{-1} = \begin{bmatrix} 0.1 & 0 \ 0.8 & 1 \end{bmatrix} $$

Consider this matrix: $\newline$ $\left[\begin{array}{cc} 10 & 0 \\ -8 & 1 \end{array}\right]$ $\newline$ Find the inverse of the matrix. Give exact values. Non-integers can be given as decimals or as simplified fractions.

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Consider this matrix:\newline[10amp;0−8amp;1] \left[\begin{array}{cc} 10 &amp; 0 \\ -8 &amp; 1 \end{array}\right] [10−8​amp;0amp;1​]\newlineFind the inverse of the matrix. Give exact values. Non-integers can be given as decimals or as simplified fractions.

Consider this matrix: $\newline$ $\left[\begin{array}{cc} 10 & 0 \\ -8 & 1 \end{array}\right]$ $\newline$ Find the inverse of the matrix. Give exact values. Non-integers can be given as decimals or as simplified fractions.