Recent content by Incognitopad

sorry. typo. i meant to write a 4. adding columns/rows into others don't change the determinant, but multiplying a row/column multiplies the determinant by the same factor. 3*4*6 72det(A)=det(B)

oh, is it that simple? 3*5*6det(A)=det(B)?

Homework Statement Consider the matrices A = a1 a2 a3 b1 b2 b3 c1 c2 c3 and B = 3a1 4a2+5a1 6a3 3b1 4b2+5b1 6b3 3c1 4c2+5c1 6c3 How are the determinants of A and B related? DO NOT COMPUTE det(A)! Homework Equations The Attempt at a...

bump :(

Homework Statement I'm given a 4x5 matrix with one missing column. I'm also given the RREF form with no missing columns. Previous parts of the question made me find the row, column, and null basis for the matrix. Now it's asking: d) Find the missing column. (Hint: Are the columns of...

yeah, its just originally without writing it out i assumed (BA)^2 was equal to B^2 * A^2 need to get used to matrix multiplication.

(BA)^2 = (BA)(BA) = BABA once again, WOW that was easy = B(AB)A = B(In)A = B(In*A) = B(A) = BA thanks mark.

Homework Statement A square matrix P is called an idempotent if P^2 = P, Show that if A is n x m and B is m x n, and if AB = In, then BA is an idempotentHomework Equations The Attempt at a Solution I have this one identity I think, but I'm not sure how to use it? If A is m x n, then ImA = A...

Uhhh... ah.. Q^2 = ((I + (I - P) A) P) * ((I + (I - P) A) P) = Ok, I'm just going to leave it expanded. Too complicated this way = (P + AP - PAP)^2 = (PP + PAP - PPAP + APP + APAP - APPAP - PAPP - PAPAP + PAPPAP) = (P + PAP - PAP + AP + APAP - APAP - PAP - PAPAP + PAPAP) = (P + AP - PAP) wow...

Homework Statement A square matrix P is called an idempotent if P^2 = P, Show that if P is an idempotent, so is Q = (P + AP - PAP) for any square matrix A (of the same size as P). Homework Equations The Attempt at a Solution basically I factor, Q = (I + (I - P) A) P then I square it and...

Homework Statement A converging lens with a focal length of 30cm and a diverging lens with a focal length of -64cm are 139cm apart. A 4.0cm tall object is 50cm in front of the converging lens. distance between image and diverging lens has been calculated to be -32cm, and it is right...