Question

The inverse of the matrix 2,1,1,3 is

Answer 1

Answer:

this is answer for your question

Answer 2

Answer:

The inverse of the matrix 2,1,1,3 is $\frac{1}{5}$$\left[\begin{array}{cc}3 & -1\\-1 & 2\end{array}\right]$

Step-by-step explanation:

• Given, Matrix A =$\left[\begin{array}{ccc}2&1\\1&3\end{array}\right]$

• |A∣ = 5

Now, adj A=$C^{T}$$\left[\begin{array}{ccc}3& -1\\-1&2\end{array}\right] ^{T}$

⇒ adj A = $\left[\begin{array}{ccc}3&-1\\-1&2\end{array}\right]$

• Hence $A^{-1}$ = $\frac{1}{5}$$\left[\begin{array}{ccc}3 & -1\\-1 & 2\end{array}\right]$

• The inverse of a square matrix A, denoted by $A^{-1}$, is the matrix that  gives the identity matrix when multiplied with the original matrix A.
• The size of the identity matrix is same size as matrix A.
• To find the inverse of a 2x2 matrix, first we have to swap the positions of a and d, put negatives in front of b and c, and then divide everything by the determinant (ad-bc).