Which of the following matrices is equal to $3\begin{bmatrix}2 & 0 \\ 0 & 5\end{bmatrix}-\begin{bmatrix}3 & 1 \\ 0 & 2\end{bmatrix}$?

$\begin{bmatrix}3 & -1 \\ 0 & 13\end{bmatrix}$

$\begin{bmatrix}3 & 1 \\ 0 & 13\end{bmatrix}$

$\begin{bmatrix}3 & -1 \\ 0 & 17\end{bmatrix}$

$\begin{bmatrix}9 & -1 \\ 0 & 28\end{bmatrix}$

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Vectors and matrices — ACT practice questions

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Practice 49 Vectors and matrices questions in the app

What this topic is

Vectors and matrices appear in ACT Mathematics as fairly direct calculation questions.

The magnitude of a vector comes from the Pythagorean theorem, so a vector with components three and four has length five. Matrices are added entry by entry, multiplied by a number by scaling every entry, and multiplied together only when the number of columns in the first equals the number of rows in the second.

Questions may also set two matrices equal and ask for the unknown entries, since equal matrices match in every position. Answer choices often show matrices with a single entry changed, so a careful check of each position matters.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Easier

What is the magnitude of the vector $⟨ - 6, 8 ⟩$ ?

2✗ Not this one10✓ Correct14✗ Not this one100✗ Not this one

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Answer: B — 10

Magnitude is $\sqrt{(- 6)^{2} + 8^{2}} = \sqrt{36 + 64} = \sqrt{100} = 10$ .

Question 2Easier

Which of the following matrices is equal to $3 [\begin{array}{cc} 2 & 0 \\ 0 & 5 \end{array}] - [\begin{array}{cc} 3 & 1 \\ 0 & 2 \end{array}]$ ?

[\begin{array}{cc} 3 & - 1 \\ 0 & 13 \end{array}]

✓ Correct

[\begin{array}{cc} 3 & 1 \\ 0 & 13 \end{array}]

✗ Not this one

[\begin{array}{cc} 3 & - 1 \\ 0 & 17 \end{array}]

✗ Not this one

[\begin{array}{cc} 9 & - 1 \\ 0 & 28 \end{array}]

✗ Not this one

Show answer

Answer: A — $[\begin{array}{cc} 3 & - 1 \\ 0 & 13 \end{array}]$

Scale first: $3 [\begin{array}{cc} 2 & 0 \\ 0 & 5 \end{array}] = [\begin{array}{cc} 6 & 0 \\ 0 & 15 \end{array}]$ . Subtracting entry by entry gives $6 - 3 = 3$ , $0 - 1 = - 1$ , $0 - 0 = 0$ , and $15 - 2 = 13$ .

Question 3Mid

If $[\begin{array}{cc} 1 & 2 \\ 0 & 1 \end{array}] [\begin{array}{c} a \\ b \end{array}] = [\begin{array}{c} 7 \\ 3 \end{array}]$ , what is the value of $a + b$ ?

1✗ Not this one3✗ Not this one4✓ Correct7✗ Not this one

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Answer: C — 4

The second row gives $b = 3$ . Then $a + 2 b = 7$ , so $a = 1$ and $a + b = 4$ .

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 49 Vectors and matrices questions in the app

Vectors and matrices — ACT practice questions

What this topic is

Sample questions

More ACT topics

Mathematics