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# 1 find all the values of t r if any such that the

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1. Find all the values of t R (if any) such that the matrix A is singular. 2. Consider the subspace spanned by the columns of A W = span { c 1 ( A ) , c 2 ( A ) , c 3 ( A ) } . Find a vector equation and a general equation of W for t = 0. 3. Find all the values of t R (if any) such that det( A ) - tr( A ) - ∥ r 1 ( A ) 2 - ( c 1 ( A ) · c 2 ( A )) t 2 = 0 2.2 Finding the equation of a line using determinants Consider the points A (1 , 2) and B (3 , 4) of the plane R 2 . 1. What is the equation of the line passing through A and B ? 2. Verify that an equivalent equation is given by x y 1 1 2 1 3 4 1 = 0 . 3. Given two generic points P ( x 1 , y 1 ) and Q ( x 2 , y 2 ) of R 2 , verify that the equation of the line passing through P and Q is x y 1 x 1 y 1 1 x 2 y 2 1 = 0 . Nancy Khalil, Spring 2018 Homework 5, page 3/4

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MATH 232 Applied Linear Algebra Legend (for “type” of question): RE = Routine Exercise: This is something you should be able to do in your sleep ;-). Your goal is to be able to answer these questions quickly and accurately every time. These form the foundations of your skill set. TC = Time Challenge: Speed and accuracy are important factors in solving this type of routine exercise. Try to do these exercises within the time limit, usually 5 minutes. If you need more time than that, it’s o.k., but keep practicing! Solving these routine exercises provides a foundation for solving more involved problems, and is essential in performing well on quizzes and exams. WP = Word Problem: Translating words into expressions (also known as modeling): Master this skill now, we will be using this all term.
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