Q1: If you multiply the matrix $$\begin{pmatrix} 1 & 0 & 0 \ 0 & 0 & 1 \ 0 & 1 & 0 \end{pmatrix}$$ from left to a matrix $A \in \mathbb{R}^{3 \times 5}$, what will happen?

A1: The second and third row of $A$ will be exchanged.

A2: Nothing. The restult will be $A$ again.

A3: The first and second row of $A$ will be exchanged.

A4: The first and second column of $A$ will be exchanged.

A5: The last row $A$ will be deleted.

Q2: If you multiply the matrix $$\begin{pmatrix} 1 & 0 & 0 \ 2 & 1 & 0 \ 0 & 0 & 1 \end{pmatrix}$$ from left to a matrix $A \in \mathbb{R}^{3 \times 5}$, what will happen?

A1: The second row of $A$ will be replaced by a new row which is given as: ‘second of $A$ + 2 times first row of $A$’

A2: Nothing. The restult will be $A$ again.

A3: The second row of $A$ will be replaced by a new row which is given as: ’third of $A$ + 2 times second row of $A$'

A4: The first and second column of $A$ will be exchanged.

A5: The second row of $A$ is replaced by the first row of $A$.

Q3: If you multiply the matrix $$\begin{pmatrix} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 0 \end{pmatrix}$$ from left to a matrix $A \in \mathbb{R}^{3 \times 5}$, what will happen?

A1: The last row of $A$ will be deleted.

A2: Nothing. The restult will be $A$ again.

A3: The second row of $A$ will be replaced by a new row which is given as: ’third of $A$ + 2 times second row of $A$'

A4: The first and second column of $A$ will be exchanged.

A5: The second row of $A$ is replaced by the first row of $A$.