GATE CS 2015 Set 2 — Question 57
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Engineering Mathematics → Linear Algebra → Matrices & Determinants
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Question
Perform the following operations on the matrix
(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 _________.
(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 _________.
Correct answer
0 to 0
Solution
Let the matrix be . The determinant of a matrix remains unchanged under row addition operations () and column subtraction operations (). Therefore, the determinant of the resultant matrix is equal to the determinant of the original matrix.Observe the relationship between Column 1 () and Column 3 ():
Thus, . Since two columns are linearly dependent (proportional), the determinant of the matrix is 0.
Thus, . Since two columns are linearly dependent (proportional), the determinant of the matrix is 0.
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