Consider this matrix: [[-4,0],[-10,-6]] 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:  [[-4,0],[-10,-6]] 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 given by [[a, b], [c, d]], we use the formula for the inverse of a 2x2 matrix: 1/(ad - bc) * [[d, -b], [-c, a]]. First, we need to calculate the determinant ad - bc.Determinant calculation: The determinant of our matrix [[-4,0],[-10,-6]] is calculated as (-4)*(-6) - (0)*(-10).Find inverse matrix: The determinant is (-4)*(-6) - (0)*(-10) = 24 - 0 = 24.Multiply by reciprocal: Now that we have the determinant, we can find the inverse by multiplying the reciprocal of the determinant by the matrix [[d, -b], [-c, a]]. For our matrix, a = -4, b = 0, c = -10, and d = -6. So the matrix [[d, -b], [-c, a]] becomes [[-6, 0], [10, -4]].Calculate inverse matrix: Multiplying the reciprocal of the determinant, which is 1/24, by the matrix [[-6, 0], [10, -4]] gives us the inverse matrix. We perform the multiplication for each element of the matrix.Simplify fractions: The inverse matrix is 1/24 * [[-6, 0], [10, -4]] which simplifies to [[-6/24, 0/24], [10/24, -4/24]].Final inverse matrix: Simplify the fractions in the matrix to get [[-1/4, 0], [5/12, -1/6]]. This is the inverse of the original matrix.

Consider this matrix: $\newline$ $\left[\begin{array}{cc} -4 & 0 \\ & \\ -10 & -6 \end{array}\right]$ $\newline$ Find the inverse of the matrix. Give exact values. Non-integers can be given as decimals or as simplified fractions.

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