1 of 8 0-day streak

Use row and column matrices of ones to extract totals

Question 1 of 8

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The data matrix \(Q\) gives the numbers of practice sessions completed by several ensembles, with one row for each ensemble and one column for each section

Row order: Senior band, Jazz group. Column order: Repertoire, Technique

Q = \begin{bmatrix} 11 & 4 \\ 3 & 3 \end{bmatrix}

The following row and column matrices of 1s are available

R = \begin{bmatrix} 1 & 1 \end{bmatrix}, \qquad C = \begin{bmatrix} 1 \\ 1 \end{bmatrix}

(a)1 mark

Which statement correctly finds the total for each row of \(Q\)?

Put the 1 by 2 row \(\begin{bmatrix} 1 & 1 \end{bmatrix}\) on the right of \(Q\)

\(Q\begin{bmatrix} 1 \\ 1 \end{bmatrix} = \begin{bmatrix} 15 \\ 6 \end{bmatrix}\) gives the totals for the columns of \(Q\)

Multiply on the right by the 2 by 1 column \(\begin{bmatrix} 1 \\ 1 \end{bmatrix}\): \(Q\begin{bmatrix} 1 \\ 1 \end{bmatrix} = \begin{bmatrix} 15 \\ 6 \end{bmatrix}\)

Multiply on the left by the 1 by 2 row \(\begin{bmatrix} 1 & 1 \end{bmatrix}\): \(\begin{bmatrix} 1 & 1 \end{bmatrix}Q = \begin{bmatrix} 14 & 7 \end{bmatrix}\)

(b)2 marks

Calculate the column matrix containing the total for each row of \(Q\)

Row totals of \(Q\)