Matrices Test

Result

Matrices Test - 46

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Weekly Quiz Competition

Question 1
1 / -0

Inverse of $$\begin{bmatrix} -1 & 5 \\ -3 & 2 \end{bmatrix}$$ is

A
$$\begin{bmatrix} 2/13 & -5/13 \\ 3/13 & -1/13 \end{bmatrix}$$

B
$$\begin{bmatrix} -2/13 & 5/13 \\ -3/13 & 1/13 \end{bmatrix}$$

C
$$\begin{bmatrix} 2 & -5 \\ 3 & -1 \end{bmatrix}$$

D
$$Cannot\ be\ determined$$

Solution
Question 2
1 / -0

If $$A$$ and $$B$$ are square matrices such that $$B=-A^{-1}BA$$, then

A
$$AB+BA=0$$

B
$$(A+B)^{o}=A^{2}+B^{2}$$

C
$$(A+B)^{2}=A^{2}+2AB+B^{2}$$

D
$$(A+B)^{2}=A+B$$

Solution
Question 3
1 / -0

If $$A=\left[ \begin{matrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{matrix} \right] $$ and $$10B=\left[ \begin{matrix} 4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3 \end{matrix} \right] $$ where $$B=A^{-1}$$ then $$\alpha$$ is equal to-

A
$$2$$

B
$$-1$$

C
$$-2$$

D
$$5$$

Solution
Question 4
1 / -0

A is a $$2\times 2$$ matrix such that $$A\begin{bmatrix} 1 & \\ & -1 \end{bmatrix}=\begin{bmatrix} 1 & \\ 0 & \end{bmatrix}$$ and $${ A }^{ 2 }\begin{bmatrix} 1 & \\ & -1 \end{bmatrix}=\begin{bmatrix} 1 & \\ 0 & \end{bmatrix}$$. The sum of the elements f A, is

A
-1

B
0

C
2

D
5
Question 5
1 / -0

The inverse of the matrix $$\left[ \begin{array} { c c c } { 1 } & { 0 } & { 0 } \\ { 3 } & { 3 } & { 0 } \\ { 5 } & { 2 } & { - 1 } \end{array} \right]$$ is

A
$$- \dfrac { 1 } { 3 } \left[ \begin{array} { c c c } { - 3 } & { 0 } & { 0 } \\ { 3 } & { 1 } & { 0 } \\ { 9 } & { 2 } & { - 3 } \end{array} \right]$$

B
$$- \dfrac { 1 } { 3 } \left[ \begin{array} { c c c } { - 3 } & { 0 } & { 0 } \\ { 3 } & { - 1 } & { 0 } \\ { - 9 } & { - 2 } & { 3 } \end{array} \right]$$

C
$$- \dfrac { 1 } { 3 } \left[ \begin{array} { c c c } { 3 } & { 0 } & { 0 } \\ { 3 } & { - 1 } & { 0 } \\ { - 9 } & { - 2 } & { 3 } \end{array} \right]$$

D
$$- \dfrac { 1 } { 3 } \left[ \begin{array} { c c c } { - 3 } & { 0 } & { 0 } \\ { - 3 } & { - 1 } & { 0 } \\ { - 9 } & { - 2 } & { 3 } \end{array} \right]$$

Solution
Question 6
1 / -0

If $$A$$ is a $$2\times 2$$ matrix such that $$A^{2}-4A+3I=0$$, then the inverse of $$A+3I$$ is equal to

A
$$\dfrac{1}{24}S-\dfrac{7}{24}I$$

B
$$\dfrac{1}{21} A-\dfrac{7}{21}I$$

C
$$\dfrac{7}{24}I+\dfrac{1}{24}A$$

D
$$A-3I$$`

Solution
Question 7
1 / -0

Let A be a $$3\times 3$$ matrix such that
$$A\left[ \begin{matrix} 1 & 2 & 3 \\ 0 & 2 & 3 \\ 0 & 1 & 1 \end{matrix} \right] =\left[ \begin{matrix} 0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{matrix} \right] $$ Then $${ A }^{ -1 }$$.

A
$$\left[ \begin{matrix} 1 & 2 & 3 \\ 0 & 1 & 1 \\ 0 & 2 & 3 \end{matrix} \right] $$

B
$$\left[ \begin{matrix} 3 & 1 & 2 \\ 3 & 0 & 2 \\ 1 & 0 & 1 \end{matrix} \right] $$

C
$$\left[ \begin{matrix} 3 & 2 & 1 \\ 3 & 2 & 0 \\ 1 & 1 & 0 \end{matrix} \right] $$

D
$$\left[ \begin{matrix} 0 & 1 & 3 \\ 0 & 2 & 3 \\ 1 & 1 & 1 \end{matrix} \right] $$
Question 8
1 / -0

If $$A=\left[ \begin{matrix} cos\theta & -sin\theta \\ sin\theta & cos\theta \end{matrix} \right] { A }^{ 1 }$$ is given by:

A
$$-A$$

B
$${ A }^{ 1 }$$

C
$${ -A }^{ 1 }$$

D
$$A$$

Solution
Question 9
1 / -0

If a , b and c are all different from zero such that $$\dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c} = 0$$, then the matrix A = $$\begin{vmatrix} 1 + a & 1 & 1 \\ 1 & 1 + b & 1 \\ 1 & 1 & 1 + c \end{vmatrix}$$ is -

A
symmetric

B
non-singular

C
can be written as sum of a symmetric and a skew symmetric matrix

D
none of these

Solution
Question 10
1 / -0

If $$\begin{bmatrix} 1 & -\tan { \theta } \\ \tan { \theta } & 1 \end{bmatrix}{ \begin{bmatrix} 1 & -\tan { \theta } \\ \tan { \theta } & 1 \end{bmatrix} }^{ -1 }={ \begin{bmatrix} \cos { \alpha } & -\sin { \alpha } \\ \sin { \alpha } & \cos { \alpha } \end{bmatrix} }^{ -1 }$$, then $$\alpha $$=

A
$$0$$

B
$$\frac { \pi }{ 2 } $$

C
$$\frac { \pi }{ 4 } $$

D
$$\frac { \pi }{ 6 } $$

Solution