Consider this matrix: [[-7,0],[-6,3]] Find the inverse of the matrix. Give exact values. Non-integers can be given as decimals or as simplified fractions.

Question

Consider this matrix:  [[-7,0],[-6,3]] Find the inverse of the matrix. Give exact values. Non-integers can be given as decimals or as simplified fractions.

Bytelearn · Accepted Answer

Identify Matrix Elements: To find the inverse of a 2x2 matrix given by [[a, b], [c, d]], we use the formula for the inverse of a matrix: [[d, -b], [-c, a]] / (ad - bc) First, we identify a, b, c, and d from our matrix [[-7,0],[-6,3]]. Here, a = -7, b = 0, c = -6, and d = 3.Calculate Determinant: Next, we calculate the determinant of the matrix, which is ad - bc. Determinant = (-7)(3) - (0)(-6) Determinant = -21 - 0 Determinant = -21Check Non-Zero Determinant: Now, we check if the determinant is non-zero, because a matrix has an inverse only if its determinant is non-zero. Since the determinant is -21, which is not equal to zero, the matrix does have an inverse.Apply Inverse Matrix Formula: We apply the formula for the inverse of a 2x2 matrix using the values of a, b, c, and d we identified earlier. Inverse matrix = [[3, -0], [6, -7]] / (-21)Simplify Inverse Matrix: We simplify the inverse matrix by dividing each element by the determinant -21. Inverse matrix = [[3 / -21, 0 / -21], [6 / -21, -7 / -21]] Inverse matrix = [[-1/7, 0], [-2/7, 1/3]]

Consider this matrix: $\newline$ $\left[\begin{array}{cc} -7 & 0 \\ -6 & 3 \end{array}\right]$ $\newline$ Find the inverse of the matrix. Give exact values. Non-integers can be given as decimals or as simplified fractions.

Full solution

More problems from Find inverse functions and relations

Related topics

Consider this matrix:\newline[−7amp;0−6amp;3] \left[\begin{array}{cc} -7 &amp; 0 \\ -6 &amp; 3 \end{array}\right] [−7−6​amp;0amp;3​]\newlineFind the inverse of the matrix. Give exact values. Non-integers can be given as decimals or as simplified fractions.

Consider this matrix: $\newline$ $\left[\begin{array}{cc} -7 & 0 \\ -6 & 3 \end{array}\right]$ $\newline$ Find the inverse of the matrix. Give exact values. Non-integers can be given as decimals or as simplified fractions.