Question

Find the inverse matrix or type "none". (use decimals) {11 -5 3 -1}

Answer 1

The inverse of the matrix  $\left[\begin{array}{cc}11&-5\\3&-1\end{array}\right]$ is the matrix $\left[\begin{array}{cc}\frac{-1}{4} &\frac{5}{4} \\\\\frac{-3}{4} &\frac{11}{4} \end{array}\right]$ .

The inverse of a matrix A is calculated by the formula:

A' = (1/|A|)(Adj A),

where A' represents the inverse of matrix A,

|A| represents the determinant value of matrix A, and

Adj A represents the Adjoin matrix of matrix A.

So, to calculate the inverse of the matrix  $\left[\begin{array}{cc}11&-5\\3&-1\end{array}\right]$ , we will first calculate its Adj.

Adj = $\left[\begin{array}{cc}-1&-3\\5&11\end{array}\right] ^{T}$= $\left[\begin{array}{cc}-1&5\\-3&11\end{array}\right]$.

Now, we calculate |A| = 11*(-1) - (-5)*3 = -11 + 15 = 4.

Therefore A' = (1/|A|)(Adj A),

or, A' = $(1/4)*\left[\begin{array}{cc}-1&5\\-3&11\end{array}\right]$ ,

or, A' = $\left[\begin{array}{cc}\frac{-1}{4} &\frac{5}{4} \\\\\frac{-3}{4} &\frac{11}{4} \end{array}\right]$ .

Therefore, the inverse of the matrix  $\left[\begin{array}{cc}11&-5\\3&-1\end{array}\right]$ is the matrix $\left[\begin{array}{cc}\frac{-1}{4} &\frac{5}{4} \\\\\frac{-3}{4} &\frac{11}{4} \end{array}\right]$ .

Learn more about the inverse of a matrix at

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