Section5.1.pdf - MAT 0AA2 Tutorial 2[10 I Given two matrices[5 3 2 \u22122 \u22121 3 3 A = 1 5 3 B = 0 \u22121 2 \u22121 0 1 2 1 4 Use the row method or the column

# Section5.1.pdf - MAT 0AA2 Tutorial 2[10 I Given two...

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MAT 0AA2 18/02/2015 Tutorial 2 [10] I. Given two matrices [5] A = 3 2 - 2 1 5 3 - 1 0 1 B = - 1 3 3 0 - 1 2 2 1 4 Use the row method or the column method to find 1. the second column of AB 2. the third row of AB 3. Express the matrix E below as a linear com- bination of the matrices A and B E = 9 - 5 - 13 2 13 0 - 8 - 3 - 10 1
II. Given two matrices [5] M = 1 1 0 1 0 2 0 2 - 3 and R = h k 1 1 i 1. Find all values of k , if any, that satisfy the equation RMR T = 0 2. Express the matrix C = 0 1 - 1 as a linear combination of columns of M 3. Compare Tr( M ) and Tr( M T )
Section 5.1: Eigenvalues and eigen- vectors Examples Example Compute the following matrix multiplications: 1. " 3 1 1 3 # " 1 1 # 2. " 1 0 0 - 1 # " 0 1 # 3. " 1 0 0 - 1 # " 1 0 # 4. 8 - 9 4 3 - 4 3 - 3 3 1 1 2 3 Do you notice anything interesting? 2
Definitions Definition If A is an n × n matrix, then a nonzero vector x in R n is called an eigenvector of A if A x is a scalar multiple of x , i.e., A x = λ x for some scalar λ . The scalar λ is called an eigen- value of A and x is said to be an eigenvector cor- responding to λ .