Answer:
a = 5
Step-by-step explanation:
We are given 3 x 3 matrix and the determinant of the matrix is -19.
We need find the value of "a" in the given matrix.
determinant (D) = -6[(-3)(-3) − (4)(4)] − 7[a(-3) − (4)(-6)] + 1[a(4) − (-3)(-6)]
-19 = -6[9 - 16] -7[-3a +24] +1[4a - 18]
-19 = -6[-7] +21a - 168 + 4a - 18
-19 = 42 + 21a -168 + 4a - 18
Simplify the like terms, we get
-19 = 25a - 144
25a = -144 + 19
25a = 125
Dividing both sides by 25, we get
a =
a = 5
So the value of a is 5.