The system 3x - 2y = 7, x + 4y = 5 is written as AX = B with matrix X. What is A?

Question 79

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The system $3x - 2y = 7$ , $x + 4y = 5$ is written as $AX = B$ with $X = \begin{bmatrix} x \\ y \end{bmatrix}$ . What is $A$ ?

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

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

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\begin{bmatrix}3 & -2 & 7 \\ 1 & 4 & 5\end{bmatrix}

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\begin{bmatrix}7 \\ 5\end{bmatrix}

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CorrectNot quiteAnswer B

Correct answer: B

$A$ holds the coefficients, one row per equation: row 1 is $3, -2$ and row 2 is $1, 4$ .
$B = \begin{bmatrix} 7 \\ 5 \end{bmatrix}$ holds the right sides.

Worth noting

The transpose puts each variable's coefficients in a row; but $AX$ multiplies a row of $A$ by the column $X$ , so each row must be one equation.

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