Question

What is the identity matrix for a row replacement?

A) Diagonal matrix
B) Zero matrix
C) Unit matrix
D) Scalar matrix

Answer 1

The identity matrix for a row replacement is the unit matrix.

Step-by-step explanation:

The identity matrix for a row replacement is C) Unit matrix.

An identity matrix is a square matrix in which all the elements of the principal diagonal are ones and all other elements are zeros. In the context of row replacement, a unit matrix is used to replace a row, meaning that the row will remain unchanged. This is because when the unit matrix is multiplied by any matrix, it does not alter the values in that row.

For example, if we have a matrix A and we replace one of its rows with the corresponding row of the unit matrix I, the resulting matrix will have the same values in that row as the original matrix A.