determine the value of h such that the matrix is the augment

determine the value of h such that the matrix is the augmented matrix of a linear system with infinitely many solutions

[5 -7|2

15 h|6]

thank you

Solution

divide scond row by -3 then

[5 -7|2

15 h|6]

=

[5 -7|2

-5 -h/3|-2]
now to have infinite solution, second row must be wiped ou by first.

replace R2 with R2+R1

[5 -7|2

0 -h/3-7|0]

-h/3-7=0 i.e. h=-21