Introduction to Matrices Flashcards

All 5 cards in this deck

What does it mean to say a matrix has order $2 \times 1$?

It has 2 rows and 1 column (a column matrix).

What are the steps to multiply a matrix by a scalar?

e.g. $3\begin{pmatrix} 1 & 2 \\ 0 & 4 \end{pmatrix}$

1. Multiply every element by the scalar: $3\times1$, $3\times2$, $3\times0$, $3\times4$

2. Write the results in the same positions: $\begin{pmatrix} 3 & 6 \\ 0 & 12 \end{pmatrix}$

Write down the $2 \times 2$ identity matrix $I$.

$I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$

Writing only "$I$" or "identity" is not accepted without this matrix.

What is the result of multiplying a $2 \times 2$ matrix $M$ by the identity matrix $I$?

$M$ itself, since $MI = IM = M$.

True or false? $\begin{pmatrix} -1 & 0 \\ 0 & -1 \end{pmatrix}$ is the identity matrix.

False. That is $-I$; the identity matrix is $\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$.