Question

let A be a 3 x 3 matrix and suppose that matrix B is obtained from A by the following row operations R1 implies that R2 , R3__R3 +5R2 if det A =12 what is det B?

a) -60
b) -12
c) 12
d) 60​

Answer 1

The det B is (d) 60. As multiply 5 with 12.

Answer 2

Answer:

-12

Step-by-step explanation:

Matrix B is obtained from Matrix A by the following elementary row operations:

1. Interchanging two rows: R₁ ↔ R₂

2. Replacing the row by adding a multiple of another row to itself: R₃→ R₃ + 5R₂

Let us now understand the effect these two Elementary Row Operations will have on the determinant of matrix A:

1. Interchanging Rows

When the two rows of a matrix are interchanged, the determinant of the newly formed matrix is obtained by multiplying (-1) to the original matrix

i.e., det (B) = - det (A)

2. Adding a multiple of another row to itself

When a row of a matrix is replaced by its addition to a multiple of another row, the determinant of new matrix is same as that of the original matrix

i.e., det (B) = det (A)

So the overall change in the determinant is: det (B) = - det (A)

⇒ det (B) = -12