A farmer in Guyana records the weekly harvest of cassava and plantains from two fields in matrices. Field 1: P = $\begin{pmatrix} 45 & 32 \ 28 & 51 \end{pmatrix}$ kg. Field 2: Q = $\begin{pmatrix} 38 & 45 \ 33 & 29 \end{pmatrix}$ kg. What is the total harvest P + Q?

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Question

A farmer in Guyana records the weekly harvest of cassava and plantains from two fields in matrices. Field 1: P = $\begin{pmatrix} 45 & 32 \ 28 & 51 \end{pmatrix}$ kg. Field 2: Q = $\begin{pmatrix} 38 & 45 \ 33 & 29 \end{pmatrix}$ kg. What is the total harvest P + Q?

Accepted Answer

$\begin{pmatrix} 83 & 77 \ 61 & 80 \end{pmatrix}$ — Award 1 mark for correctly adding corresponding elements to obtain (45+38, 32+45; 28+33, 51+29) = (83, 77; 61, 80). B is incorrect — it shows P − Q (subtraction instead of addition). C is incorrect because elements are placed in wrong positions. D is incorrect because it shows 2P (scalar multiplication) instead of P + Q.

Answer

$\begin{pmatrix} 7 & -13 \ -5 & 22 \end{pmatrix}$

Answer

$\begin{pmatrix} 83 & 61 \ 77 & 80 \end{pmatrix}$

Answer

$\begin{pmatrix} 90 & 64 \ 56 & 102 \end{pmatrix}$

Answer

$\begin{pmatrix} 83 & 77 \ 61 & 80 \end{pmatrix}$

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