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6. Determinants
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Q16 of 256 Page 7

A matrix A of order 3 × 3 has determinant 5. What is the value of |3A|?

If the determinant of a matrix A of order m is ∆, then the determinant of matrix λA, where λ is a scalar, is λm∆.

In this question, ∆=5, λ=3 and m=3.


|λA|=33×5


=135


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14

If A = [aij] is a 3 × 3 scalar matrix such that a11 = 2, then write the value of |A|.

15

If I3 denotes identity matrix of order 3 × 3, write the value of its determinant.

17

On expanding by first row, the value of the determinant of 3 × 3 square matrix A = [aij] is a11C11 + a12C12 + a13C13, where Cij is the cofactor of aij is the cofactor of aij in A. Write the expression for its value of expanding by second column.

18

Let A = [aij] be a square matrix of order 3 × 3 and Cij denote cofactor of aij in A. If |A| = 5, write the value of a31C31 + a32C32 + a33C33.

Questions · 256
6. Determinants
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