Unformatted text preview: Show that A is not invertible. ( Hint : construct a 3 × 3 invertible matrix B such that det( AB ) = 0). 3. Let r 1 , r 2 and r 3 be the rows of a 3 × 3 matrix A = r 1 r 2 r 3 . Let B = 2 r 1 + 3 r 2 r 3 + 2 r 1 r 2r 13 r 3 If det( A ) = 2, ﬁnd det( B ). 4. Consider the matrix A = 12 22 1 22 3 (a) Show that λ = 1 is an eigenvalue of A . (b) Is A diagonalizable? 5. Prove or disprove (a) If λ is an eigenvalue of A , then λ is also an eigenvalue of A T . (b) If A 2 + A = 0, then λ = 1 cannot be an eigenvalue of A . (c) A 3 × 3 matrix cannot have four distinct eigenvalues. (d) An invertible matrix A can have λ = 0 as eigenvalue. (e) if λ is an eigenvalue of an invertible matrix A , then 1 λ is an eigenvalue of A1 ....
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This note was uploaded on 11/29/2010 for the course MATH 222 taught by Professor Karlpeterrussell during the Spring '08 term at McGill.
 Spring '08
 KarlPeterRussell
 Math

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