Question

Algebra 2 question? Matrices question

Answer 1

See a) to e) below

Explanation:

A matrix is just a table - in this case the headings tell you exactly what each matrix, each row and each column represent.

For example, the value `26` in the first matrix means there are `26` round-necked, small T-shirts for boys.

They are both `2 xx 3` matrices which means they have the same format so can be added or subtracted, but they are not compatible for multiplying.

a) To add the matrices - add the values in the corresponding positions - some are shown here in colour.

`A =[(color(blue)(26),19,color(red)(17)),(23,color(lime)(12),17)] +[(color(blue)(14),19,color(red)(22)),(26,color(lime)(11),23)]`

`A=[(color(blue)(40),38,color(red)(39)),(49,color(lime)(23),40)]`

Matrix A is now an array showing how many T-shirts there are altogether for each design and each size.

b) `a_21` refers to the value in the second row and first column, ie `49` This means there are `49` small V-neck T-shirts in stock.

c) Adding all the elements of the first row of matrix A will tell us how many round-necked T-shirts there are altogether in all sizes.
There are `40+38+39 =117` round-necked T-shirts in stock.

d) The number of Medium T-shirts is shown in the second column. Adding the elements in the second column of `A` gives:
`38+23 = 61` medium shirts in both styles in stock.

e) To find out how many more boys' T-shirts than girls in each size there are we need to subtract the two matrices:

`[(color(blue)(26),19,color(red)(17)),(23,color(lime)(12),17)] -[(color(blue)(14),19,color(red)(22)),(26,color(lime)(11),23)]`

`= [(color(blue)(12),0,color(red)(-5)),(-3,color(lime)(1),-6)]`

(Negative values mean there are more girls' shirts than boys'.

TO find out many there are in each size, find the total of each column:

`[(9,1,-11)]`

Therefore:
`9` more small boys' T-shirts
`1` more medium boys' T-shirt
`11` more large girls' T-shirts