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Pmidterm1[1]

# Pmidterm1[1] - MAT211 Fall 2010 Practice Midterm I The...

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Unformatted text preview: MAT211 Fall 2010 Practice Midterm I The actual midterm will consist of 6 problems. Problem 1 Consider the vectors → v = - 1 2 and → x = 3 1. Find → v + → x , → v- → x , → x- → v , proj L ( → x ) and ref L ( → x ), where the line L is collinear(parallel) to vector → v } . proj L and ref L are projection and reflection related to L . 2. Represent graphically the vectors found in 1. 1 Problem 2 Consider a linear system A → x = → b where A is a m × n matrix. You are told that this linear system always has a solution, no matter which → b you choose. 1. Can you conclude that A is invertible? 2. What can you say about the rank of A ? 2 Problem 3 For which values of a constant k is the matrix A = k 1 1 1 k 1 1 1 k invertible? Find the inverse....
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Pmidterm1[1] - MAT211 Fall 2010 Practice Midterm I The...

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