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Matrices · Question 47 of 106

Question 47

MediumOriginal question

What is [2−13][41−2]\begin{bmatrix}2 & -1 & 3\end{bmatrix}\begin{bmatrix}4 \\ 1 \\ -2\end{bmatrix}?

Options for question 47

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. A 1 × 3 matrix times a 3 × 1 matrix is a 1 × 1 matrix.

  2. Its one element is (2)(4)+(−1)(1)+(3)(−2)=8−1−6=1(2)(4) + (-1)(1) + (3)(-2) = 8 - 1 - 6 = 1.

Worth noting

The 3 × 3 matrix is the product the other way round, [41−2][2−13]\begin{bmatrix}4 \\ 1 \\ -2\end{bmatrix}\begin{bmatrix}2 & -1 & 3\end{bmatrix}.

Concept
A row times a column, and a column times a row
Typical time
90 s
Your time
—
The rule this testsMultiplication of matrices
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