Consider a linear transformation T: R2 ⟶ R3, whose matrix T. Also consider the bases β={(1,0),(0,1)} base of R2 and β′={(1,0,1),(−2,0,1),(0,1,0)} base of R3. So what's the image T(1, -3,)? Choose an option: (a) T (1,−3) = 4.(1, 0, 1) − 3.(−2, 0, 1) + 11.(0, 1, 0) (b) T (1,−3) = 4.(1, 0, 1) + 3.(−2, 0, 1) − 11.(0, 1, 0) (c) T (1,−3) = 4.(1, 0, 1) + 3.(−2, 0, 1) + 11.(0, 1, 0) (d) T (1,−3) = 4.(1, 0, 1) − 3.(−2, 0, 1) − 11(0, 1, 0) (e) T (1,−3) = −4.(1, 0, 1) − 3.(−2, 0, 1) − 11.(0, 1, 0)
Consider a linear transformation T: R2 ⟶ R3, whose matrix T. Also consider the bases β={(1,0),(0,1)} base of R2 and β′={(1,0,1),(−2,0,1),(0,1,0)} base of R3. So what's the image T(1, -3,)? Choose an option: (a) T (1,−3) = 4.(1, 0, 1) − 3.(−2, 0, 1) + 11.(0, 1, 0) (b) T (1,−3) = 4.(1, 0, 1) + 3.(−2, 0, 1) − 11.(0, 1, 0) (c) T (1,−3) = 4.(1, 0, 1) + 3.(−2, 0, 1) + 11.(0, 1, 0) (d) T (1,−3) = 4.(1, 0, 1) − 3.(−2, 0, 1) − 11(0, 1, 0) (e) T (1,−3) = −4.(1, 0, 1) − 3.(−2, 0, 1) − 11.(0, 1, 0)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 16E
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Consider a linear transformation T: R2 ⟶ R3, whose matrix T.
Also consider the bases β={(1,0),(0,1)} base of R2 and β′={(1,0,1),(−2,0,1),(0,1,0)} base of R3. So what's the image T(1, -3,)?
Choose an option:
(a) T (1,−3) = 4.(1, 0, 1) − 3.(−2, 0, 1) + 11.(0, 1, 0)
(b) T (1,−3) = 4.(1, 0, 1) + 3.(−2, 0, 1) − 11.(0, 1, 0)
(c) T (1,−3) = 4.(1, 0, 1) + 3.(−2, 0, 1) + 11.(0, 1, 0)
(d) T (1,−3) = 4.(1, 0, 1) − 3.(−2, 0, 1) − 11(0, 1, 0)
(e) T (1,−3) = −4.(1, 0, 1) − 3.(−2, 0, 1) − 11.(0, 1, 0)
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