Matrices and Determinants Part 1

From the given system, we have
‌

k+1

k

=‌

8

k+3

≠‌

4k

3k−1

( as System has no solution)
⇒k2+4k+3=8k
⇒k=1,3
If k=1 then ‌

8

1+3

≠‌

4.1

2

which is false
And if k=3
Then ‌

8

6

≠‌

4.3

9−1

which is true, therefore k=3
Hence for only one value of k.
System has no solution.