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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
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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).
 Fall '05
 HUI
 Linear Algebra, Algebra, Vectors

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