sample_tt1_1_ans

sample_tt1_1_ans - Math 136 Term Test 1 Answers NOTE: -...

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

View Full Document Right Arrow Icon
Math 136 Term Test 1 Answers NOTE : - Only answers are provided here (and some proofs). On the test you must provide full and complete solutions to receive full marks. 1. Short Answer Problems a) List the 3 elementary row operations. Solution: 1. Multiply a row by a non-zero constant 2. Swap two rows 3. Add a multiple of one row to another. b) Does the spanning set span 1 2 1 , 0 1 0 , 1 0 1 represent a line or a plane in R 3 ? Give a vector equation which describes it. Solution: This is a plane with vector equation ~x = t 0 1 0 + s 1 0 1 . c) If A is an n × m matrix and B is an m × p matrix, then what is the size of AB ?. Solution: AB is n × p . d) Explain why ~a × ( ~ b × ~ c ) must be a vector in the plane with vector equation ~x = s ~ b + t~ c , s, t R . Solution: Suppose that ~n = ~ b × ~ c 6 = ~ 0. Then ~n is orthogonal to both ~ b and ~ c , so it is a normal vector to the plane through the origin that contain ~ b and ~ c . Then ~a × ( ~ b × ~ c ) = ~a × ~n is orthogonal to ~n so it lies in the plane with normal ~n , that is, in the plane containing ~ b and ~ c . Hence, for some real numbers s, t , a × ( ~ b × ~ c ) = s ~ b + t~ c since ~ b and ~ c span the plane.
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/25/2010 for the course MATH 136 taught by Professor All during the Spring '08 term at Waterloo.

Page1 / 4

sample_tt1_1_ans - Math 136 Term Test 1 Answers NOTE: -...

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