This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: deﬁned matrix C . 4. Deﬁne A = ± 1 2 3 4 ² . Find a matrix B = ± a b c d ² so that AB = I . For your answer, also ﬁnd BA . 5. Deﬁne the matrices R = ± cos(90 ◦ )sin(90 ◦ ) sin(90 ◦ ) cos(90 ◦ ) ² = ±1 1 ² , S = ± cos(45 ◦ )sin(45 ◦ ) sin(45 ◦ ) cos(45 ◦ ) ² = " √ 2 2√ 2 2 √ 2 2 √ 2 2 # , and T = ± cos(180 ◦ ) sin(180 ◦ ) sin(180 ◦ )cos(180 ◦ ) ² = ±1 0 1 ² . (a) For a vector ~x ∈ R 2 , describe geometrically the eﬀect of multiplying ~x on the left by the matrices R , S , or T . (b) Does RS = SR ? Does this make sense given your answer to part (a)? (c) Does RT = TR ? Does this make sense given your answer to part (a)?...
View
Full
Document
This note was uploaded on 03/30/2011 for the course MATH 152 taught by Professor Caddmen during the Spring '08 term at UBC.
 Spring '08
 Caddmen
 Math

Click to edit the document details