Add and subtract matrices

Stock at start (A)

\(\displaystyle \begin{bmatrix}14&9\\11&16\end{bmatrix}\)

Sold during the week (B)

\(\displaystyle \begin{bmatrix}6&4\\8&7\end{bmatrix}\)

A surf shop has two branches, North and South (rows). It stocks boards and wetsuits (columns). Matrix A holds the stock at the start of the week and matrix B holds the stock sold during the week. How many wetsuits does the South branch have left at the end of the week?

Rows are Front then Back counters; columns are coffee then tea. Move Tuesday's Front coffee count below and above Monday's 24. Compare the entries in B − A and A − B

For every position of the slider, which entries moved, and how did the two difference matrices compare?

Add and subtract matrices

Two matrices of the same order combine entry by entry at matching positions. For A - B, take the entry of B from the entry of A at every position

1. 1Check the order Addition and subtraction are defined only when both matrices have the same number of rows and columns \(\displaystyle A:2\times3,\quad B:2\times3\quad\Rightarrow\quad A\pm B\text{ is defined}\)
2. 2Match positions Combine each entry only with the entry at the same row and column \(\displaystyle (A-B)_{22}=a_{22}-b_{22}\)
3. 3Keep the subtraction direction For A - B, subtract the entry of B from the entry of A at every position \(\displaystyle (A-B)_{22}=a_{22}-b_{22}\)
4. 4Keep the common order The result has the same order as the two matrices being combined \(\displaystyle A,B:2\times3\quad\Rightarrow\quad A-B:2\times3\)

Stock at start (P)

\(\displaystyle \begin{bmatrix}40&25&32\\36&18&27\end{bmatrix}\)

Sold in spring (S)

\(\displaystyle \begin{bmatrix}22&19&30\\15&12&9\end{bmatrix}\)

Delivered in spring (D)

\(\displaystyle \begin{bmatrix}10&15&12\\8&20&6\end{bmatrix}\)

A plant nursery has two sites, Eastside and Hilltop (rows), and sells natives, herbs and succulents (columns). P is the stock at the start of spring, S is the stock sold in spring and D is the stock delivered in spring. How many herbs are at Hilltop at the end of spring?

Find the Hilltop herbs position in each matrix, then work start minus sold plus delivered

Stock at start (P)

\(\displaystyle \begin{bmatrix}40&25&32\\36&18&27\end{bmatrix}\)

Sold in spring (S)

\(\displaystyle \begin{bmatrix}22&19&30\\15&12&9\end{bmatrix}\)

Delivered in spring (D)

\(\displaystyle \begin{bmatrix}10&15&12\\8&20&6\end{bmatrix}\)

Rows are Eastside then Hilltop; columns are natives, herbs then succulents. Find the net change in succulent stock at Eastside from deliveries and sales alone

Delivered minus sold, at the Eastside succulents position

Stock at start (A)

\(\displaystyle \begin{bmatrix}14&9\\11&16\end{bmatrix}\)

Sold during the week (B)

\(\displaystyle \begin{bmatrix}6&4\\8&7\end{bmatrix}\)

Which line correctly calculates the entry in row 2, column 2 of A minus B?