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35 votes
35 votes

Perform the following operations on the matrix $\begin{bmatrix} 3 & 4 & 45 \\ 7 & 9 & 105 \\ 13 & 2 & 195 \end{bmatrix}$

  1. Add the third row to the second row
  2. Subtract the third column from the first column.

The determinant of the resultant matrix is _____.

4 Answers

Best answer
45 votes
45 votes
Answer $0$, because it is easy to see that first column and third column are multiple of each other.

Third column $=$ First column $^{\ast }15.$

So rank is  $< 3$, so Determinant must be $0$.

It stays zero as row & column transformations don't affect determinant.
edited by
27 votes
27 votes
Ans Zero, row and column transformations doesn't affect determinant.
1 votes
1 votes
Only interchanging two rows or two columns determinant value becomes -ve .Except any elementary operation doesn't affect determinant.

Answer  0

1 votes
1 votes

If two rows of a matrix are interchanged, the determinant changes sign. If a multiple of a row/column is subtracted from another row/column, the value of the determinant is unchanged.

so Det(A)=0 as after taking common 15  from  column 3  column 1 and column 3 become identical so Det(A)=0.

Answer=0

Answer:

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