Question

इस ए इज ए नॉनसिंगुलर स्क्वायर मैट्रिक्स आफ ऑर्डर 3 एंड ए स्क्वायर इक्वल टू 2 दिन फाइंड द वैल्यू ऑफ मोटे​

Answer 1

Step-by-step explanation:

Let A = [ a ij ] be a square matrix. The transpose of the matrix whose ( i, j) entry is the a ij cofactor is called the classical adjoint of A:

Example 1: Find the adjoint of the matrix

The first step is to evaluate the cofactor of every entry:

Therefore,

Why form the adjoint matrix? First, verify the following calculation where the matrix A above is multiplied by its adjoint:

Now, since a Laplace expansion by the first column of A gives

equation (*) becomes

This result gives the following equation for the inverse of A:

By generalizing these calculations to an arbitrary n by n matrix, the following theorem can be proved:

Theorem H. A square matrix A is invertible if and only if its determinant is not zero, and its inverse is obtained by multiplying the adjoint of A by (det A) −1. [Note: A matrix whose determinant is 0 is said to be singular; therefore, a matrix is invertible if and only if it is nonsingular