1 of 8 0-day streak

Use row and column matrices of ones to extract totals

Question 1 of 8

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Matrix \(N\) records the numbers of seedlings planted in several community gardens. Each row represents one garden; each column represents one seedling type

Row order: School garden, Park garden, Creek garden, Station garden. Column order: Lettuce, Tomatoes, Herbs, Beans

N = \begin{bmatrix} 4 & 10 & 5 & 7 \\ 3 & 11 & 5 & 4 \\ 7 & 5 & 11 & 12 \\ 12 & 5 & 8 & 10 \end{bmatrix}

The following row and column matrices of 1s are available

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

(a)1 mark

Select the ones matrix and side that produce all row totals of \(N\)

Multiply on the left by the 1 by 4 row \(\begin{bmatrix} 1 & 1 & 1 & 1 \end{bmatrix}\): \(\begin{bmatrix} 1 & 1 & 1 & 1 \end{bmatrix}N = \begin{bmatrix} 26 & 31 & 29 & 33 \end{bmatrix}\)

Put the 1 by 4 row \(\begin{bmatrix} 1 & 1 & 1 & 1 \end{bmatrix}\) on the right of \(N\)

Multiply on the right by the 4 by 1 column \(\begin{bmatrix} 1 \\ 1 \\ 1 \\ 1 \end{bmatrix}\): \(N\begin{bmatrix} 1 \\ 1 \\ 1 \\ 1 \end{bmatrix} = \begin{bmatrix} 26 \\ 23 \\ 35 \\ 35 \end{bmatrix}\)

\(N\begin{bmatrix} 1 \\ 1 \\ 1 \\ 1 \end{bmatrix} = \begin{bmatrix} 26 \\ 23 \\ 35 \\ 35 \end{bmatrix}\) gives the totals for the columns of \(N\)

(b)4 marks

Use right multiplication by a column of 1s to find all row totals of \(N\)

Row totals of \(N\)