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#### Application of Matrices and Determinants One Mark Questions

12th Standard EM

Reg.No. :
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Maths

Time : 00:30:00 Hrs
Total Marks : 10
5 x 1 = 5
1. If A is a 3 × 3 non-singular matrix such that AAT = ATA and B = A-1AT, then BBT =

(a)

A

(b)

B

(c)

I

(d)

BT

2. If A = $\left[ \begin{matrix} 7 & 3 \\ 4 & 2 \end{matrix} \right]$, then 9I - A =

(a)

A-1

(b)

$\frac { { A }^{ -1 } }{ 2 }$

(c)

3A-1

(d)

2A-1

3. If A = $\left[ \begin{matrix} 3 & 1 & -1 \\ 2 & -2 & 0 \\ 1 & 2 & -1 \end{matrix} \right]$ and A-1 = $\left[ \begin{matrix} { a }_{ 11 } & { a }_{ 12 } & { a }_{ 13 } \\ { a }_{ 21 } & { a }_{ 22 } & { a }_{ 23 } \\ { a }_{ 31 } & { a }_{ 32 } & { a }_{ 33 } \end{matrix} \right]$ then the value of a23 is

(a)

0

(b)

-2

(c)

-3

(d)

-1

4. Let A be a 3 x 3 matrix and B its adjoint matrix If |B|=64, then |A|=

(a)

±2

(b)

±4

(c)

±8

(d)

±12

5. If AT is the transpose of a square matrix A, then

(a)

|A| ≠ |AT|

(b)

|A| = |AT|

(c)

|A| + |AT| =0

(d)

|A| = |AT| only

6. 5 x 1 = 5
7. $\rho$(A) = $\rho$[(A|B]) =2 < number of unknowns

8. (1)

9. $\rho$(A) = $\rho$[(A|B]) = 1  < number of unknowns

10. (2)

Consistent with one parameter family of solution

11. $\rho$(A) ≠ $\rho$[(A|B])

12. (3)

Consistent with two parameter family of solution

14. (4)

|A|n-1