Recent content by NeonVomitt

Homework Statement Let A be a 3 x 3 matrix with determinant 14. Then detadj(A^T) =___, det (adj)(A^-1) =___ and det((adj)(7A)) = ___ Homework Equations Thank you! If someone could show me the steps that would be swell! The Attempt at a Solution

that is what RREF does anyways. So if, [ -2 -3 ] [ 0 -6] [1 3/2 ] [0 -6 ] [ 1 3/2 ] [ 0 1 ] [1 0 ] [0 1 ] Is that not the answer in four elementary matrix steps for the first question? And for the second question it is the same, but steps on the other side...

Homework Statement I don't know why I keep getting this wrong...some help would be greatly appreciated. A = [ 0 -6 ] [-2 -3 ] (1) Write A as a product of 4 elementary matrices: Wouldn't that just mean to Reduce Row echelon it, and show it in 4 steps? (2) Write A^-1 as a...

Which of these formulas hold for all invertible n x n matrices A and B: 1) 8A is invertible 2) A + B is invertible 3) (A + B)^2 = A^2 + B^2 + 2AB 4) (ABA^1)^7 = AB^7A^1 5) (AB)^-1 = A^-1B^-1 6) ABA^-1 = B Thanks

Homework Statement Prove or disprove the following statements concerning 2 x 2 matrices. (a) If A^3 = 5I then A is invertible. (b) If A and B are both invertible then AB - BA is not invertible. (c) If ABC = I then B is invertible. (d) If A^2 - 3A -2I = 0 then (A-1) and (A-2I) are both...

Suppose that v1,v2,v3 are linearly independent vectors in R^5 and consider the vectors a1,a2,a3 defined by a1=v1+v2-2v3, a2=3v1+v2+4va, and a3=v1+2v2-7v3. Show that at least one of the vectors v1,v2,v3 is not in the span of the vectors a1,a2,a3. I am kind of confused. Should I somehow reduce...

If I want to find if span ([4, 0, -3], [2,2,1]) = span ([2,-2,-4], [0,1,5]) do I first find their reduced row echelon form, and then see if they match? For instance, if I found both matrices to reduce to: [ 1 0] [ 0 1] [ 0 0] does that mean that they equal each other? Or do I have to...