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### Matrix and Determinant

10. the value of $|\begin{array}{ccc}2& 3& 4\\ 5& 6& 7\\ 10& 12& 14\end{array}|$ is [2075]

10

15

0

20

11. If A = (1,2,3) and b = $\left(\begin{array}{c}1\\ 2\\ 3\end{array}\right)$ then AB is [2075]

4

14

0

15

12. The inverse of the matrix $|\begin{array}{cc}-1& 1\\ 1& -3\end{array}|$ is [2075]

$|\begin{array}{cc}-3& 1\\ 1& -1\end{array}|$

$\frac{1}{2}$ $|\begin{array}{cc}-3& -1\\ -1& -1\end{array}|$

$|\begin{array}{cc}-3& -1\\ 1& 1\end{array}|$

$\frac{1}{2}$ $|\begin{array}{cc}-1& 1\\ 1& -3\end{array}|$

10. If A = $\left(\begin{array}{c}1\\ 2\\ 3\end{array}\right)$ and B = ± $\left(\begin{array}{ccc}1& 2& 3\end{array}\right)$ then AB is [2074]

$\left(\begin{array}{cc}1& 49\end{array}\right)$

$\left(\begin{array}{cc}1& 4\end{array}\right)$

$0$

$\left(\begin{array}{ccc}1& 2& 3\\ 2& 4& 6\\ 3& 6& 9\end{array}\right)$

11. Value of $\left[\begin{array}{ccc}0& 2& 3\\ 1& 2& 3\\ 4& 8& 12\end{array}\right]$ is [2074]

10

1

0

-1

12. Matrix $\left(\begin{array}{ccc}1& 2& 3\\ -1& 0& 4\\ -3& -4& 5\end{array}\right)$ is [2074]

Diagonal

Symmetric

Skew Symmetric

unit

10. If $\left[\begin{array}{ccc}k& 1& 0\\ 2& 0& k\\ 0& 2& -1\end{array}\right]$ = 0, then k = [2073]

1

-1

0

± 1

11. The value of x for which A = $\left[\begin{array}{cc}6& x-3\\ 3& x\end{array}\right]$ has no inverse is [2073]

0

1

-2

2

10. If A = $\left(\begin{array}{ccc}-1& 0& 2\end{array}\right)$ and B = $\left(\begin{array}{c}2\\ 3\\ 4\end{array}\right)$, then AB is [2072]

6

0

(-2 0 8)

(2 0 -4)

11. The value of the determinant $\left[\begin{array}{ccc}1& 2& 0\\ 2& 4& 1\\ 3& 6& 2\end{array}\right]$ is [2072]

1

3

0

4

12. The adjoint of the matrix abcd is [2072]

$\left(\begin{array}{cc}a& d\\ b& c\end{array}\right)$

$\left(\begin{array}{cc}a& b\\ d& c\end{array}\right)$

$\left(\begin{array}{cc}a& d\\ c& b\end{array}\right)$

$\left(\begin{array}{cc}d& \mathrm{-b}\\ \mathrm{-c}& a\end{array}\right)$

8. If $A=\left[\begin{array}{cc}1& 2\\ 2& 3\end{array}\right]$ , then A2 - nA - I = 0, then the value of n is [2071]

0

4

1

-4

9. If $A=\left[\begin{array}{ccc}1& 0& 1\\ 0& 1& 1\\ 1& 0& 0\end{array}\right]$ , then A is [2071]

Symmetric

Skew-Symmetric

Singular

Non Singular

4. If A = , then A100 is equal to [2070]

1

0

-1

None

I there is