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Unformatted text preview: (b) Solve the linear system A x = . Hint: The solutions should de-pend on the parameter ╬╗ ; use the ´Čürst part to determine how. 4. Assuming det a b c p q r x y z = 7, evaluate det a + 3 p b + 3 q c + 3 r 5 x 5 y 5 z-p-q-r . 5. An invertible matrix A is said to be orthogonal if A-1 = A T . (a) If A is an orthogonal matrix, what are the only two possible values for det A ? Justify. (b) Consider R ╬▒ the matrix of rotation of angle ╬▒ counterclockwise. Find R-1 ╬▒ and R T ╬▒ . Is R ╬▒ orthogonal? Compute det R ╬▒ . (c) Consider F ╬▓ the matrix of re´Čéection across a line making an an-gle of ╬▓ with the x-axis. Find F-1 ╬▓ and F T ╬▓ . Is F ╬▓ orthogonal? Compute det F ╬▓ . 2...
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This note was uploaded on 03/30/2011 for the course MATH 152 taught by Professor Caddmen during the Spring '08 term at UBC.
- Spring '08