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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 rst 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 reection 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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- Spring '08