Mid2PracticeSol

Mid2PracticeSol - Math 20F A00 Linear Algebra Spring 2011...

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Unformatted text preview: Math 20F A00, Linear Algebra, Spring 2011 Practice Problems for Midterm Exam 2 1. Find all the co-factors, the adjugate matrix, and the determinant of the matrix 1 1 2- 1 2- 4 1- 1 0 2- 1 0 2 . 2. True or false: (a) Equivalent matrices have the same determinant; (F) (b) The determinant of any elementary matrix is 1; (F) (c) det( A + B ) = det A + det B , det(- A ) =- det A, and det( AB ) = (det A )(det B ); (F, F, T) (d) det A T = det A and det A- 1 = (det A )- 1 ; (T, T) (e) A square matrix is invertible if and only if its determinant is nonzero. (T) 3. Calculate the determinant of each of the following matrices: 5- 1 1- 3- 2 5 3 ; 1 1 2- 1- 4- 1 3 12 1 2- 4 1 ; 1 3 3- 4 1 2 5 2 5 4- 3- 3- 7- 5 2 . 4. Show that det 1 1 1 a b c a 2 b 2 c 2 = ( a- b )( b- c )( c- a ). (Hint: transpose, row reduction, and expan- sion.) 5. Let A, B, C be three 2 × 2 matrices. Show that det bracketleftbigg A B C bracketrightbigg = (det A )(det C )....
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This note was uploaded on 11/20/2011 for the course MATH 20 C taught by Professor Ronevans during the Spring '08 term at UCSD.

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Mid2PracticeSol - Math 20F A00 Linear Algebra Spring 2011...

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