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..Example:
Find the adjoint of the matrix. ..
Find the adjoint of the matrix. ..Note 1:
Only a square matrix can have its invers..
Note 3:
Inverse of A is denoted by A - 1 , thus B = A - 1 and AA - 1 = A - 1 A=..
Theorem
If A and B are two invertible matrices of the same order, then (AB) - 1 = B - 1 A - 1..
Theorem
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..Definition
Let R i denotes the i t h row of the matrix A = [a i j ] then the elementary row operations on the matrix A are defined as: 3. R i g R i + kR j means multiply each element of j t h row by k and add it to the corresponding elements of i t h row. The corresponding column transformatio..
Let R i denotes the i t h row of the matrix A = [a i j ] then the elementary row operations on the matrix A are defined as: 3. R i g R i + kR j means multiply each element of j t h row by k and add it to the corresponding elements of i t h row. The corresponding column transformatio..Non-singular Matrix
A square matrix A is said to be non-singular if its determinant value is non-zero. i.e.,..
A square matrix A is said to be non-singular if its determinant value is non-zero. i.e.,..Properties of Inverse of Matrix
In other words, a square matrix A is invertible if and only if A is a non-singular matrix. (c) If A and B are invertible square matrices, then (AB) - 1 = B - 1 A - 1 (d) If A and B are two non-singular square matrices of the same order, then AB and BA are also non-singular matrices of th..
In other words, a square matrix A is invertible if and only if A is a non-singular matrix. (c) If A and B are invertible square matrices, then (AB) - 1 = B - 1 A - 1 (d) If A and B are two non-singular square matrices of the same order, then AB and BA are also non-singular matrices of th..See what our Users say :
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