Midterm1practice

# Midterm1practice - following matrix. How are their...

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NAME: Math 415 — Midterm 1 practice Total points: 100 . Please show your work and explain all answers. Cal- culators, computers, books and notes are not allowed. Suggestion: even if you cannot complete a problem, write out the part of the solution you know. You can get partial credit for it. 1. [20 points] Calculate the determinant of the following matrix: 1 0 1 1 2 1 0 1 1 - 1 0 - 1 4 0 1 1 1

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NAME: 2. [20 points] Find the inverse of the following matrix using Gauss-Jordan reduction. 1 1 1 1 2 2 2 1 2 2
NAME: 3. [20 points] Find bases for the range, corange, and nullspace of the

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Unformatted text preview: following matrix. How are their dimensions related? 1 1 2 1 1 0-1 1 1 2 0 1-2-1 3 NAME: 4. [20 points] Solve the following linear system. x 1 + x 2 + x 3 + x 4 = 1 x 1 + x 3 + 2 x 4 = 2 x 1 + x 2 + x 4 = 3 4 NAME: 5. [20 points] Consider the vectors v 1 = ( x-1) , v 2 = ( x 2-1) , v 3 = ( x +1) , and v 4 = x 2 . Can you choose some or all of them to be a basis for P (2) ? Prove your answer. 5...
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## This note was uploaded on 02/10/2009 for the course MATH 415 taught by Professor Bertrandguillou during the Spring '08 term at University of Illinois at Urbana–Champaign.

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Midterm1practice - following matrix. How are their...

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