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Unformatted text preview: A of this transformation. Geometrically, what kind of transformation is this? 4. (10 pts) Find the matrix for re±ection across the plane x + y2 z = 0. Is this matrix invertible? 5. (12 pts) Determine whether the following statements are true or false. If the statement is true, explain your reasoning. If the statement is false then Fnd a counterexample. (a) Suppose that A is an n × n matrix and ~v is a vector in R n such that the system A~x = ~v has no solutions. Then the system A~x = ~ 0 will have inFnitely many solutions. (b) If A , B and C are NONZERO 2 × 2 matrices and AB = AC then B = C . (c) If A is a 2 × 2 matrix and A 2 = I 2 then A = I 2 . (d) If two matrices A and B have the same shape and the same rank, then each can be obtained from the other by a sequence of elementary row operations....
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This note was uploaded on 04/28/2008 for the course MAT 202 taught by Professor Staff during the Spring '08 term at Princeton.
 Spring '08
 Staff
 Math, Linear Algebra, Algebra

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