assig9_2011

assig9_2011 - (b) Solve the linear system A x = . Hint: The...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 152, Spring 2011 Assignment #9 Notes: Each question is worth 5 marks. Due in class: Monday, March 14 for MWF sections; Tuesday, March 15 for TTh sections. Solutions will be posted Tuesday, March 15 in the afternoon. No late assignments will be accepted. 1. Let T : R 2 R 2 be the linear transformation defined by T ( x,y ) = (2 x - 3 y, 4 x - 5 y ). (a) Write the matrix A that corresponds to T . (b) Calculate the determinant of A . (c) Is A invertible? If yes, calculate its inverse. 2. Consider the following 5 × 5 matrices: M = 1 3 - 7 6 0 0 1 3 - 3 0 0 2 - 1 3 0 0 3 6 3 2 0 1 0 1 0 , N = 1 0 0 0 0 6 2 0 0 0 π 2 - 1 0 0 2 21 36 2 0 74 45 π 52 1 . (a) Compute det M . (b) Compute det N . (c) Compute det( N 2 M T N - 1 M 3 ). (d) If the matrices M and N had been previously entered into MAT- LAB, write the MATLAB command to compute the value found in part (c). 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
3. (a) Find all values of λ for which the matrix A = 1 0 - λ - 1 3 1 0 2 λ - 4 is not invertible.
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Page1 / 2

assig9_2011 - (b) Solve the linear system A x = . Hint: The...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online