Question

Given that a= (4) and b= (2)
(7) (4)
If

Answer 1

x = 12, y = 20

Explanation:

Given

4a - 2b

= 4
`\left[\begin{array}{ccc}4\\7\\\end{array}\right]` - 2
`\left[\begin{array}{ccc}2\\4\\\end{array}\right]` ← multiply each component by the scalar

=
`\left[\begin{array}{ccc}4(4)\\4(7)\\\end{array}\right]` -
`\left[\begin{array}{ccc}2(2)\\2(4)\\\end{array}\right]`

=
`\left[\begin{array}{ccc}16\\28\\\end{array}\right]` -
`\left[\begin{array}{ccc}4\\8\\\end{array}\right]` ← subtract corresponding components

=
`\left[\begin{array}{ccc}16-4\\28-8\\\end{array}\right]`

=
`\left[\begin{array}{ccc}12\\20\\\end{array}\right]` =
`\left[\begin{array}{ccc}x\\y\\\end{array}\right]`

with x = 12 and y = 20