Problem 6 5 pts a b b Given the following matrix A a a b a a

Problem 6 (5 pts) a b b Given the following matrix: A a a b a a a (a) If b 0, A is triangular. Uill in the blank) (1 pt) (b) Prove that A is invertible if a 0 and a b. (Hint: Find the pivots or A 1) (4 pts)

Solution

a) As upper triangular elements are zero, Its a lowertriangular matrix.

b) Determinant of A=a³+b²a-2ba² not equal to zero. So A is invertible.

verifying in matlab;

a=1;
b=0;
A=[a b b;a a b;a a a];

A^-1

Result;

1 0 0
-1 1 0
0 -1 1