Question

· Let A = [aij] be a square matrix of order 3/3 and A=-7. The value of a11 A21 + a12 A22 + a13 A23 Where Aij is the cofactor of element aij b. 1 d. 3 a. O c.2​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

Let $\sf{A = [a_{ij}] }$ be a square matrix of order 3 × 3 and det A = - 7 .

The value of $\sf{a_{11} A_{21} + a_{12} A_{22} + a_{13} A_{23} }$

Where $\sf{A_{ij}}$ is the cofactor of element $\sf{a_{ij} }$

a. 0

b. 1

c. 2

d. 3

EVALUATION

We know that if $\sf{A = [a_{ij}] }$ is a square matrix of order n and $\sf{A_{ij}}$ is the cofactor of element $\sf{a_{ij} }$

Then

$\sf{a_{i1} A_{k1} + a_{i2} A_{k2} + .. + a_{in} A_{kn} = 0 \: \: \: \: where \: \: i \ne \: k}$

Here it is given that A is a square matrix of 3

Thus n = 3

Now take i = 1 & k = 2

Then i ≠ k

So From above we get by putting i = 1 , k = 2 , n = 3

$\sf{a_{11} A_{21} + a_{12} A_{22} + a_{13} A_{23} = 0 }$

FINAL ANSWER

Hence the correct option is a. 0

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