If a
matrix B is obtained from a matrix A by multiplying every row of A by

, then

.

Question

If a 
  matrix B is obtained from a matrix A by multiplying every row of A by 
  
, then 
  
.

Quizplus · Accepted Answer

Multiplying every row of a matrix by a scalar results in a matrix with the same number of rows and the same column entries scaled by the scalar. Therefore, the dimensions of matrix B will be the same as matrix A, and the entries in each row will be scaled by the given scalar. Therefore, the determinant of matrix B may be larger or smaller than the determinant of matrix A, depending on the scalar value and the original entries of matrix A.

If a Matrix B Is Obtained from a Matrix a a Matrix