Sp07_midterm2

# Sp07_midterm2 - Name Discussion Section No PID Time Midterm...

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Name: PID: Discussion Section - No: Time: Midterm 2, Math 20F - Lecture B (Spring 2007) Duration: 50 minutes This is a closed-book exam. Calculators are not allowed. You can use one page of notes. To get full credit you should support your answers unless otherwise is stated. There are four questions in this exam. 1. An n × n matrix A is called skew-symmetric if A T = - A . Specifically the set of 2 × 2 skew-symmetric matrices is given by S 2 × 2 = 0 - a a 0 : a R . Let T : L 2 × 2 S 2 × 2 be the transformation from the 2 × 2 lower triangular matrices onto the 2 × 2 skew-symmetric matrices defined as T b 0 a c = 0 - a a 0 . where a , b , c are real numbers. a) (1 point) Show that S 2 × 2 is a one-dimensional subspace of 2 × 2 matrices. Find a basis for this subspace. b) (2 points) Show that T is a linear transformation. # Score 1 2 3 4 Total

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c) (2 points) Find a basis for the kernel of T . 2. (Each part is 1 point) Determine whether each of the following statements is true or false. For each part circle either T (true) or F (false).
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