MATH 1004 Study Guide - Midterm Guide: Scalar Multiplication, Linear Map, Augmented Matrix

• School: Carleton University
• Department: Mathematics
• Course: MATH 1004
• Professor: All

Document Summary

Student no (in ink): a)[2] let be a basis for where. If the coordinate vector of relative to the basis is. Ans: b)[2] let the transformation matrix of the transformation. Give the c)[2] let be a linear transformation. Ans: d)[2] let the transformation rotate points about origin through an angle of radians. B2 72,41b xb 35 x 11723415x22: t 100124: t 21)(ut 53)(vt)23(vut 43532213)(2)(3)23(vtutvut22: t3/ t )3/sin()3/cos(01 t )3/cos()3/sin(10 t 2/12/32/32/1)3/cos()3/sin()3/sin()3/cos( 34: t 2341111t 3512011t)( xt 4215x 003200100001~421520111111 20113111124215x 5952011311112)(ttxthn hn ohh u vh vuhh uhc uchso the standard matrix is e)[2] [2] let be a linear transformation s. t. Ans: a subset satisfied. of of is called a subspace if all the following 3 properties are (i)the zero vector is in (ii) is close under addition. (or, for each and in. , the sum is in (iii) is in is close under scalar multiplication. (or, for each in and each scalar.