precalc

[mattflint50]

let A be any 2X2 matrix and r be a real number. show that det rA=r^2 det A

can someone give me a little help

 

[tkhunny]

What does 'rA' mean? Would it help to know that for A a 3x3 matrix, det(rA) = r³*det(A)?

1) Find the determinant of A.

2) Multiply EACH element in 'A' by 'r'. That's what 'rA' means.

3) Find the determinant of 'rA'.

4) Observe what pops out.

 

[elchichita]

det is a linear operator by rows or columns, so you can "pull out" r twice (one per row) of det(rA) to get det(rA)=r^2 det A