Question

show tha determinant x+3 x x
x x+3 x
x x x+3 is equal to 27(x+1)
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Answer 1

Step-by-step explanation:

(x+3) (x) (x)

(x) (x+3) (x)

(x) (x) (x+3)

R1 → R1 -R2 & then R2→ R2 -R3

3 0 x

-3 3 x

0 -3 x+3

Now, determinant = 3[3(x+3) - (-3)x] - 0 + x[(-3)(-3)-0]

= 3[3x+9+3x] +9x

= 18x +27+9x

= 27(x+1). Proved