104k views
2 votes
Multiply by the scalar (1 over the determinant): A^(-1) = a11 a12 a21 a22 a11 = a12 = a21 = a22 =

A. a11, a12, a21, a22
B. a11/a11, a12/a11, a21/a11, a22/a11
C. a11/a11, a12/a12, a21/a21, a22/a22
D. a11/a22, a12/a22, a21/a22, a22/a22

User Arathunku
by
7.0k points

1 Answer

5 votes

Final answer:

The question requires calculating the inverse of a 2x2 matrix multiplied by the scalar 1 over the determinant. However, the provided options merely suggest dividing matrix elements by a scalar, which by itself would not produce an inverse matrix. Therefore, none of the options given are correct for finding the inverse of a matrix.

Step-by-step explanation:

The question pertains to finding the inverse of a 2x2 matrix multiplied by the scalar 1 over the determinant of the matrix. The given matrix A^(-1) = a11 a12 a21 a22 has elements a11, a12, a21, and a22. When we multiply by the scalar (1/det(A)), where det(A) represents the determinant of matrix A, each element of the inverse matrix A^(-1) is scaled by that amount.

To obtain The inverse of a matrix, you need to perform certain operations. However, the options given do not represent the full process of finding the inverse of a matrix due to the lack of a transpose of the cofactor, among other missing elements. Instead, the provided options suggest merely dividing elements of a matrix by a scalar, which alone would not yield an inverse matrix.

Therefore, none of the given options, B, C, or D are correct expressions for the inverse of a matrix when multiplied by the scalar 1 over the determinant. Typically, to find the inverse of a 2x2 matrix, you would swap the elements a11 and a22, change the signs of a12 and a21, and then multiply each by 1 over the determinant.

User Art F
by
7.5k points