Answer:
p = - [tex]\frac{1}{2}[/tex] , q = 15
Step-by-step explanation:
Evaluate left side and equate to right side
4d - c
= 4 [tex]\left[\begin{array}{ccc}p\\2\\\end{array}\right][/tex] - [tex]\left[\begin{array}{ccc}-3\\q\\\end{array}\right][/tex]
multiply each element by 4
= [tex]\left[\begin{array}{ccc}4p\\8\\\end{array}\right][/tex] - [tex]\left[\begin{array}{ccc}-3\\q\\\end{array}\right][/tex]
subtract the corresponding elements
= [tex]\left[\begin{array}{ccc}4p+3\\8-q\\\end{array}\right][/tex]
Now
[tex]\left[\begin{array}{ccc}4p+3\\8-q\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1\\-7\\\end{array}\right][/tex]
equate corresponding elements
4p + 3 = 1 ( subtract 3 from both sides )
4p = - 2 ( divide both sides by 4 )
p = [tex]\frac{-2}{4}[/tex] = - [tex]\frac{1}{2}[/tex]
8 - q = - 7 ( subtract 8 from both sides )
- q = - 15 ( multiply both sides by - 1 )
q = 15
