Two students buy pens, notebooks and erasers in the quantities matrix Q (one row each). The prices are ₹40, ₹25 and ₹10, written matrix P. What does each student spend, as QP?

Question 55

MediumOriginal question

Two students buy pens, notebooks and erasers in the quantities $Q = \begin{bmatrix}2 & 3 & 1 \\ 1 & 4 & 2\end{bmatrix}$ (one row each). The prices are ₹40, ₹25 and ₹10, written $P = \begin{bmatrix}40 \\ 25 \\ 10\end{bmatrix}$ . What does each student spend, as $QP$ ?

\begin{bmatrix}155 \\ 170\end{bmatrix}

Correct answerYour answer

\begin{bmatrix}175 \\ 150\end{bmatrix}

Correct answerYour answer

\begin{bmatrix}165 \\ 160\end{bmatrix}

Correct answerYour answer

\begin{bmatrix}165 \\ 150\end{bmatrix}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Each row of $Q$ times the prices: $2 \times 40 + 3 \times 25 + 1 \times 10 = 165$ .
$1 \times 40 + 4 \times 25 + 2 \times 10 = 160$ . So $QP = \begin{bmatrix} 165 \\ 160 \end{bmatrix}$ : ₹165 and ₹160.

Worth noting

Each total multiplies a row by the price column, element by element, and adds.

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