MATH 3A Midterm: Midterm_2_3A_f2015
2
MATH 3A Full Course Notes
Verified Note
2 documents
Document Summary
There are 4 exercises, worth 100 = 26 + 24 + 26 + 24 points. For c r de ne the 3 3 matrix ac by (a) compute det(ac). For which c is ac invertible? (b) compute a 1. 0 . (c) let b = [2, 4, 1]t . Use your answer from b to solve a0x = b. 15 (a) compute a basis for the null space nul(b) of b. Null(b)? (b) compute a basis for column space col(b) of b. Let c be the 3 3 matrix given by. If yes, nd such a p and d. Then the set of solutions to ax = b is a subspace of rm. (b) let b be an n n matrix. Then b is invertible if and only if the columns of. Bt span rn. (c) let c be an m n matrix. Then one has dim(col(c)) + dim(nul(c)) = m. (d) let d, e be n n matrices.
