To find the inverse of a matrix A. A=[1−2−11]

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To find the inverse of a matrix A.  A=[1−2−11]

Bentley Leach · Accepted Answer

Given: The matrix A is given by A=[1−2−11] Key concept: matrix A is invertible, i.e., the inverse of the matrix A is exist if the matrix A is non-singular, i.e., the determinant of the matrix A is not equal to zero. The inverse of the given matrix can be obtained using elementary row operations using following key-steps. Forming a new matrix of order n×n. Any of the two rows can be interchanged. The element of any row can be multiplied by a nonzero scalar constant. Any two rows can be changed by using addition or subtraction with the corresponding element row. Calculation: Determinant of matrix A is given by |A|=[1−2−11] =1−2 ∵|A|=−1≠q0 Thus, the matrix A is non-singular and hence invertible. Let us find the inverse of the given matrix using elementary row transformation. For this form anaugmented matrix of order 2×4 with the 2×2 identity matrix on the right half. [1−210−1101] Adding row 1 to row 2(R2=R2+R1), we get ∼[1−2100−111] Subtracting row 2 multiplied by 2 from row 1(R1=R1−2R2), we get ∼[10−1−20−111] Multiplying row 2 by −1(R2=−R2), we get ∼[10−1−201−1−1] Here, right side is equal to A−1. Thus, A−1=[−1−2−1−1]. Conclusion: Matrix A is non-singular, hence invertible and its inverse is given by A−1=[−1−2−1−1].

To find the inverse of a matrix A.

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