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

Question

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

Accepted Answer

Step:1 ：To find the inverse of a 2x2 matrix ( A = begin{bmatrix} a & b  c & d end{bmatrix} ), we can use the formula ( A^{-1} = frac{1}{ad-bc} begin{bmatrix} d & -b  -c & a end{bmatrix} )Step:2 ：Substitute the values into the formula, we get ( A^{-1} = frac{1}{(1)(4)-(2)(3)} begin{bmatrix} 4 & -2  -3 & 1 end{bmatrix} )Step:3 ：Simplify the fraction to get ( A^{-1} = -2 begin{bmatrix} 4 & -2  -3 & 1 end{bmatrix} )Step:4 ：Then distribute the -2 to each element in the matrix to get ( A^{-1} = begin{bmatrix} -8 & 4  6 & -2 end{bmatrix} )

Answer

Step: 1 ：To find the inverse of a 2x2 matrix ( A = begin{bmatrix} a & b  c & d end{bmatrix} ), we can use the formula ( A^{-1} = frac{1}{ad-bc} begin{bmatrix} d & -b  -c & a end{bmatrix} )Step: 2 ：Substitute the values into the formula, we get ( A^{-1} = frac{1}{(1)(4)-(2)(3)} begin{bmatrix} 4 & -2  -3 & 1 end{bmatrix} )Step: 3 ：Simplify the fraction to get ( A^{-1} = -2 begin{bmatrix} 4 & -2  -3 & 1 end{bmatrix} )Step: 4 ：Then distribute the -2 to each element in the matrix to get ( A^{-1} = begin{bmatrix} -8 & 4  6 & -2 end{bmatrix} )

Find the inverse of the matrix $A = [\begin{matrix} 1 & 2 3 & 4 \end{matrix}]$

Answer

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Find the inverse of the matrix $A = [\begin{matrix} 1 & 2 3 & 4 \end{matrix}]$