Perform the following operations on the matrix M = [[3, 4, 45], [7, 9, 105], [13, 2, 195]]:
i. Add the third row to the ...

Question

Perform the following operations on the matrix M = [[3, 4, 45], [7, 9, 105], [13, 2, 195]]:
i. Add the third row to the second row.
ii. Subtract the third column from the first column.
The determinant of the resultant matrix is ___________.

Accepted Answer

det = 0 Row and column operations on a matrix change its structure but may not change the determinant significantly. Adding one row to another preserves the determinant. Subtracting one column from another also preserves the determinant. If the resulting matrix has linearly dependent rows or columns, the determinant is 0.

Perform the following operations on the matrix M = [[3, 4, 45], [7, 9, 105], [13, 2, 195]]: i. Add the third row to the second row. ii. Subtract the third column from the first column. The determinant of the resultant matrix is ___________.