Basic matrix operations Quiz 1

Question 1

If $$A=\begin{bmatrix}   1 & -1  \   2 & -1  \ \end{bmatrix}$$ , then what is the model matrix of $$A$$?

Accepted Answer

$$\begin{bmatrix}   1 & 1  \   1-i & 1+i  \ \end{bmatrix}$$

Answer

$$\begin{bmatrix}   1 & 1  \   1+i & 1+i  \ \end{bmatrix}$$

Answer

$$\begin{bmatrix}   1 & 1  \   1-i & 1-i  \ \end{bmatrix}$$

Answer

$$\begin{bmatrix}   1 & 1  \   1+i & 1-i  \ \end{bmatrix}$$

Question 2

If $$\begin{bmatrix}   1 & 2 & -2  \   1 & 2 & 1  \   -1 & -1 & 0  \ \end{bmatrix}$$ , then what is the diagonal matrix of $$A$$?

Accepted Answer

$$\begin{bmatrix}   1 & 0 & 0  \   0 & -1 & 0  \   0 & 0 & -3  \ \end{bmatrix}$$

Answer

$$\begin{bmatrix}   1 & 0 & 0  \   0 & 2 & 0  \   0 & 0 & 3  \ \end{bmatrix}$$

Answer

$$\begin{bmatrix}   -3 & 0 & 0  \   0 & -1 & 0  \   0 & 0 & -1  \ \end{bmatrix}$$

Answer

$$\begin{bmatrix}   0 & 0 & 0  \   0 & 2 & 1  \   0 & 0 & 3  \ \end{bmatrix}$$

Question 3

Solve the following matrix: $$ \ \begin{bmatrix}   {{x}^{2}}+1 & xy & xz  \   xy & {{y}^{2}}+1 & yz  \   xz & yz & {{z}^{2}}+1  \ \end{bmatrix}$$

Accepted Answer

$$1+{{x}^{2}}+{{y}^{2}}+{{z}^{2}}$$

Answer

$$-({{x}^{2}}+{{y}^{2}}+{{z}^{2}})$$

Answer

$${{x}^{2}}+{{y}^{2}}+{{z}^{2}}-1$$

Answer

$${{x}^{2}}+{{y}^{2}}+{{z}^{2}}$$

Question 4

Solve the following matrix: $$ \ \begin{bmatrix}   -1 & -1 & -1  \   \alpha  & \beta  & \chi   \   {{\alpha }^{3}} & {{\beta }^{3}} & {{\chi }^{3}}  \ \end{bmatrix}$$

Accepted Answer

$$\left( \beta -\alpha  \right)\left( \chi -\beta  \right)\left( \alpha -\chi  \right)\left( \alpha +\beta +\chi  \right)$$

Answer

$$\left( \alpha +\beta  \right)\left( \beta +\chi  \right)\left( \chi +\alpha  \right)\left( \alpha -\beta -\chi  \right)$$

Answer

$$\left( \alpha -\beta  \right)\left( \beta -\chi  \right)\left( \chi -\alpha  \right)\left( \alpha +\beta +\chi  \right)$$

Answer

$$\left( \alpha +\beta  \right)\left( \beta +\chi  \right)\left( \chi +\alpha  \right)\left( \alpha +\beta +\chi  \right)$$

Question 5

If the inverse of a matrix is $$\begin{bmatrix}   0.2 & 0.2 & 0  \   -0.2 & 0.3 & 1  \   0.2 & -0.3 & 0  \ \end{bmatrix}$$ . What is the original matrix?

Accepted Answer

$$10	imes \begin{bmatrix}   0.3 & 0 & 0.2  \   0.2 & 0 & -0.2  \   0 & 0.1 & 0.1  \ \end{bmatrix}$$

Answer

$$ \begin{bmatrix}   0.3 & 0.3 & 0.2  \   0 & 0 & 0  \   0 & 0.1 & 0  \ \end{bmatrix} $$

Answer

$$10	imes \begin{bmatrix}   0.3 & 0 & 0.2  \   0.2 & 0 & 0.2  \   0 & -0.1 & 0.1  \ \end{bmatrix}$$

Answer

$$10	imes \begin{bmatrix}   0.3 & 0.3 & 0.2  \   0 & 0 & 0  \   0 & 0.2 & 0.1  \ \end{bmatrix}$$