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Midterm

Practice Test 4

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Department
Mathematics
Course Code
MATH 1502
Professor
Geronimo

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Description
Math 1502 Practice Test 4 Geronimo 1.a) Consider the matrices     1 2 1 0 1 2 1     i) A = 2 0 1 ii)B = 1 2 0 1 . 3 2 2 1 4 2 0 n m n m A : R → R for what n and m? B : R → Rfor what n and m? Find AB. Find A − 3I where I is the 3 × 3 identity matrix. b) Consider the matrix   1 1 −1 0 −1  1 0 1 1 0  A =  1 1 −1 1 −2  1 0 1 1 0 Find a basis for Col(A). Find a basis for Nul(A). What is rank A? For an m × n matrix A why do the pivotal columns form a basis for Col(A)? 2a. Find the eigenvalues and corresponding eigenvectors to the matrix   −3 1 1 A =  1 −3 1  1 1 −1
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