# tut4 - Math 136 Tutorial 4 Problems 12 3 1 3 1 Let A = 3...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 136 Tutorial 4 Problems 12 3 1 3 1: Let A = 3 −1, B = ,C= . −1 −1 4 21 Calculate the following or state that they don’t exist: a) AB b) CB c) C T AT . 2: Let S = {(1, 1, −1), (0, 1, −1), (2, −1, 1), (−1, 2, 3)}. a) Write the system of linear equations we would need to solve if we wanted to determine if S is linearly independent or dependent. b) Just by looking at the system of linear equations, how can you tell that S must be linearly dependent? c) By solving the system, ﬁnd two linear combinations of the vectors in S that proves that S is linearly dependent. 3: Let A be an m × n matrix. Prove that the system of linear equations Ax = b has a solution for every b ∈ Rm if and only if the rank of A = m. 4: Let S = {v1 , v2 , v3 } be a set of vectors in R3 . Prove that span S = R3 if and only if S is linearly independent. 1 ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online