Prelim 2 [Solutions]

# 32 32 b deta3 deta3 a3 det5a 53 deta 125a

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Unformatted text preview: ingle nonzero element and arrive at only taking the sum of the determinants of two 2 × 2 matrices. That is, 1010 141 711 7 1 4 1 det 1 0 7 0 =1· 0 7 0 +1· 1 0 0 362 032 0362 ￿ ￿ ￿ ￿ 11 11 =7· −1· = 7(2 − 3) + 1(2 − 3) = −6. 32 32 (b) det(A3 ) = det(A)3 = a3 . det(5A) = 53 det(A) = 125a. det(C T ) = det(C ) = c. det(AT B 2 C −1 ) = det(A) det(B )2 det(C )−1 = ab2 /c. (c) Twice the ﬁrst row plus the third row equals three times the second row. The determinant is 0. 6) (a) (9 points) If P is a projection matrix that projects vectors ￿ ∈ Rn onto a subspace v...
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## This note was uploaded on 01/30/2014 for the course MATH 2940 taught by Professor Hui during the Fall '05 term at Cornell University (Engineering School).

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