Linear Algebra Matrices / Determinant

Question

R2-2R1 R3-3R1

A ————>————> [1 0 2 0 2 a 0 0 b] 3x3 matrix.

[1 0 2 0 2 a 0 0 b] <——<———<————<————R

2R2 -5R3 R2-R3 R1+2R3

(a) Determine the values of a and b such that A is singular

(b) Suppose R = I3, the order 3 identity matrix. Write A as a product of elementary matrices.

(c) Suppose det(A) = -20 What is det(R)?

Some background info, A has undergo 2 ERO to get to the matrix [1 0 2 0 2 a 0 0 b] R also has undergo 4 ERO to get to that same matrix.

I calculated and got (a) b = 0 and a = any real number

for (c) I got det(R) to be 2. Are these correct

however I could not do (b) as I’m confused on the order to follow

Answer 1

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