Exercises: Understand Zero and Identity Matrices

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Grade 9·19 problems·~30 min·Common Core Math - HS Number and Quantity·standard·hsn-vm-c-10

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Recall / Warm-Up

Which matrix is the additive identity for $2 \times 2$ matrices?

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

$\begin{bmatrix}0&0\\0&0\end{bmatrix}$

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

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

Which matrix is the multiplicative identity $I_2$ ?

$\begin{bmatrix}0&0\\0&0\end{bmatrix}$

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

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

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

For the $2 \times 2$ matrix $A = \begin{bmatrix}a & b \\ c & d\end{bmatrix}$ , which formula gives $\det(A)$ ?

$ad + bc$

$ac - bd$

$ad - bc$

$a + b + c + d$

Let $A = \begin{bmatrix}5 & -2\\3 & 7\end{bmatrix}$ and $O = \begin{bmatrix}0&0\\0&0\end{bmatrix}$ . What is $A + O$ ?

$\begin{bmatrix}0&0\\0&0\end{bmatrix}$

$\begin{bmatrix}5&-2\\3&7\end{bmatrix}$

$\begin{bmatrix}5&0\\0&7\end{bmatrix}$

$\begin{bmatrix}10&-4\\6&14\end{bmatrix}$

Let $A = \begin{bmatrix}3&1\\2&5\end{bmatrix}$ and $I = \begin{bmatrix}1&0\\0&1\end{bmatrix}$ . Which statement is true?

$AI \neq IA$ for this matrix.

$AI = A$ and $IA = A$ .

$AI = A$ but $IA \neq A$ in general.

$AI = I$ (multiplying by $I$ gives $I$ ).

Compute $\det\begin{bmatrix}4 & 1\\2 & 3\end{bmatrix}$ .

Compute $\det\begin{bmatrix}2 & 4\\1 & 2\end{bmatrix}$ .

Find $A^{-1}$ for $A = \begin{bmatrix}3 & 1\\2 & 4\end{bmatrix}$ .

$\frac{1}{10}\begin{bmatrix}4 & -1\\-2 & 3\end{bmatrix}$

$\begin{bmatrix}1/3 & 1\\1/2 & 1/4\end{bmatrix}$

$\frac{1}{10}\begin{bmatrix}3 & 1\\2 & 4\end{bmatrix}$

$\begin{bmatrix}4 & -1\\-2 & 3\end{bmatrix}$

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