Find a non-zero 2×2 matrix such that

Question

7 -6 * a b = 0 0

-14 12 c d 0 0

Answer 1

7a-6c = 0

-14a +12c = 0

the two equations are linearly dependent

with an infinite number of solutions

same with

7b-6d = 0

-14b+12c= 0

a=6, c=7

b=6, d=7

is one solution

6 6

7 7

another is

a=12=b

c=14=d

12 12

14 14

or

18 18

21 21

or

24 24

28 28