Find the inverse of the 2x2 matrix (A = begin{bmatrix} 3 & 4 2 & 1 end{bmatrix}).

Question

Find the inverse of the 2x2 matrix (A = begin{bmatrix} 3 & 4  2 & 1 end{bmatrix}).

Accepted Answer

Step:1 ：The formula to find the inverse of a 2x2 matrix (A = begin{bmatrix} a & b  c & d end{bmatrix}) is given by (A^{-1} = frac{1}{{ad - bc}} begin{bmatrix} d & -b  -c & a end{bmatrix})Step:2 ：Here, (a = 3), (b = 4), (c = 2), and (d = 1). So, (ad - bc = 3*1 - 4*2 = -5)Step:3 ：Substitute these values into the formula to get (A^{-1} = frac{1}{{-5}} begin{bmatrix} 1 & -4  -2 & 3 end{bmatrix} = begin{bmatrix} -0.2 & 0.8  0.4 & -0.6 end{bmatrix})

Answer

Step: 1 ：The formula to find the inverse of a 2x2 matrix (A = begin{bmatrix} a & b  c & d end{bmatrix}) is given by (A^{-1} = frac{1}{{ad - bc}} begin{bmatrix} d & -b  -c & a end{bmatrix})Step: 2 ：Here, (a = 3), (b = 4), (c = 2), and (d = 1). So, (ad - bc = 3*1 - 4*2 = -5)Step: 3 ：Substitute these values into the formula to get (A^{-1} = frac{1}{{-5}} begin{bmatrix} 1 & -4  -2 & 3 end{bmatrix} = begin{bmatrix} -0.2 & 0.8  0.4 & -0.6 end{bmatrix})

Find the inverse of the 2x2 matrix \(A = \begin{bmatrix} 3 & 4 \\ 2 & 1 \end{bmatrix}\).

Answer

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