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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This note was uploaded on 09/14/2011 for the course MAT 211 taught by Professor Movshev during the Spring '08 term at SUNY Stony Brook.

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

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