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Unformatted text preview: S a subspace of R 4 ? Show work to justify your answer. (b) Find a list of vectors which span S . 5. Answer each question separately. Show work to justify your answers . (a) Suppose the matrix A = a b c p q r x y z has cofactor matrix D E F G H N J K M . What is aE + pH + xK ? (b) Try to ﬁnd two nonsingular 2 × 2 matrices A and B with ( A + B ) 2 = A 2 + B 2 . (c) If A is an n × n skew symmetric matrix and n is odd, show that A must be singular. (d) Let A = λ 1 0 λ 1 0 0 λ . Find A k for k ≥ 2. 6. Find the determinant of A = 1 + x 1 x 2 x 3 x 4 x 1 1 + x 2 x 3 x 4 x 1 x 2 1 + x 3 x 4 x 1 x 2 x 3 1 + x 4 and express your ﬁnal answer in the most compact and simpliﬁed form....
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 Spring '06
 Dr.JeffChakFuWONG
 Linear Algebra, Algebra, Vector Space, Hong Kong Department, Mathematics MAT2310B Linear, Applications Midterm Examination

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