Question

Matrix
X-py = 4
-2x+y= q
Find values of p and q for which system equations has a unique solution

Answer 1

slopes of the two lines must not be equal!!

Answer 2

\[{-1\over p}\ne{-2}\]

Answer 3

"q" can be any real number

Answer 4

x-py=4
-2x+y=q
writing in the matrix form
[■(1&-p@-2&1)][■(x@y)]=[■(4@q)]
Or AX=B
X=A-1 B
|A|=|■(1&-p@-2&1)|
|A|=1*1-(-p*-2)
=1-2p
For a unique solution |A| ≠0 i.e 1-2p≠0
1≠2p
p≠1/(2 ), q can have any value