This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: (b) Solve the linear system A x = . Hint: The solutions should depend on the parameter λ ; use the ﬁrst 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 zpqr . 5. An invertible matrix A is said to be orthogonal if A1 = A T . (a) If A is an orthogonal matrix, what are the only two possible values for det A ? Justify. (b) Consider R α the matrix of rotation of angle α counterclockwise. Find R1 α and R T α . Is R α orthogonal? Compute det R α . (c) Consider F β the matrix of reﬂection across a line making an angle of β with the xaxis. Find F1 β and F T β . Is F β orthogonal? Compute det F β . 2...
View
Full Document
 Spring '08
 Caddmen
 Math, Linear Algebra, Invertible matrix, Det, Compute det

Click to edit the document details