sample_tt1_1_ans

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

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

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.

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

View Full Document
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
Ask a homework question - tutors are online