Multiplying matrices Quiz 1

Question 1

If  $$A  = \begin{bmatrix}4 & -3 \ -2 & 11\end{bmatrix}$$ and $$B = \begin{bmatrix}a & b \ c & d \end{bmatrix} $$ and the product of these two matrices is commutative, what is $$\dfrac{(a-d )}{c}$$

Accepted Answer

3.5

Answer

2

Answer

1.5

Answer

17

Question 2

Let $$A = \begin{bmatrix}1 & 2\ 2 & 1\end{bmatrix}, $$ then :

Accepted Answer

$$A^{2}-2A-3I=0$$

Answer

$$AA^{T}=1$$

Answer

$$A^{2}-4A-3I=0$$

Answer

None.

Question 3

Given functions $$F(x) = \begin{bmatrix}\cos x  & \sin x\ -\sin x & \cos x \end{bmatrix}$$ and $$G(x) =\begin{bmatrix}\cos x  & -\sin x\ \sin x & \cos x\end{bmatrix}$$  and  $$[F(x)G(x)]$$ is an identity matrix, what is the value of $$x$$?

Accepted Answer

$$\dfrac{(n\pi )}{4}$$

Answer

n

Answer

$$\dfrac{(\pi )}{2}$$

Answer

$$\dfrac{((2n+1)\pi )}{2}$$

Question 4

If A is a square matrix of order n and is idempotent and orthogonal, what is the type of this matrix $$(A+A^{T})(A-A^{T})$$ where $$A^{T}$$ is this transpose?

Accepted Answer

Skew -Symmetric.

Answer

Symmetric.

Answer

Nilpotent.

Answer

Skew-Hermitian.

Question 5

Imagine two position vectors are given as $$\vec{a}=3\hat{i}+4\hat{j}+\hat{k}$$ and $$\vec{b}=\hat{i}+6\hat{j}-\hat{k}$$ , evaluate a vector which is served by a magnitude of $$2$$ units such that this vector is perpendicular to their resultant.Given matrices $$A = \begin{bmatrix}2^{n}&-3^{n}&0 \ 3^{n}&2^{n}&0 \ 0&0&1\end{bmatrix},B= \begin{bmatrix}2^{n}&0&3^{n} \ 0&1&0 \-3^{n}&0&0\end{bmatrix}, \left | AB ight |$$ is a multiple of

Accepted Answer

9

Answer

6

Answer

2

Answer

7