q1S04 - A of this transformation. Geometrically, what kind...

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Name Class Time MATH 202 - QUIZ # 1 Due Wednesday, February 25 at 2PM Covers Chapters 1 and 2 of the text Time: 60 minutes Please show all work. Books, notes, calculators, are not permitted on this quiz. As part of your obligations under the Honor Code, do not discuss this quiz with anyone until after the Wednesday 2PM deadline. WRITE OUT AND SIGN THE PLEDGE: I pledge my honor that I have not violated the Honor Code during this examination.
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1. (8 pts) Find all solutions to the given system by using elementary row operations to bring the matrix of the system into reduced row echelon form. Be sure to indicate which variables are free variables and which are leading variables. x + 2 y + u + v + 3 w = 0 2 x + 4 y + 5 u + 2 v + 3 w = 0 3 x + 6 y + 3 u - 4 v + 2 w = 0
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2. (10 pts) Find all vectors ~ b so that the system below is solvable. Interpret your answer geo- metrically. 2 x 1 - x 2 + 4 x 3 = b 1 x 1 + x 2 - x 3 = b 2 7 x 1 + x 2 + 5 x 3 = b 3
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3. (10 pts) Let T ( ~x ) = A~x be a linear transformation from R 2 to R 2 and suppose that T " 3 2 # = " 3 2 # and T " 7 5 # = " 7 5 # + " 3 2 # = " 10 7 # Find the matrix
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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 + y-2 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.

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q1S04 - A of this transformation. Geometrically, what kind...

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