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MAT2114 HOMEWORK 06 3. Let B be a basis for R³ and let v = A (a) Find [v], the coordinate vector of v with respect to the B-basis. [v]B= (b) Suppose T: R3 R2 is the linear transformation satisfying Find T(v). T(b₁)= -1-2 T(ba)= -[2]. T(b)-| - HINT: IN PART (a) YOU FOUND THE COORDINATES OF v. WHAT ARE THOSE COORDINATES ACTUALLY COMMUNICATING TO YOU ABOUT THE RELATIONSHIP BETWEEN V AND B? The 5-43 V₂ 11 2x3-3-1 2+1 T(v) = [13] 10-12-12 2 1476-8 MAT2114 HOMEWORK 06 (c) Find the standard matrix [T] for the transformation 7: R R2 in part (b). NOTE: SIMILAR TO PART (B), DOING THIS WILL REQUIRE YOU TO FIGURE OUT HOW TO WRITE EACH OF THE STANDARD BASIS VECTORS AS LINEAR COMBINATIONS OF THE B-BASIS VECTORS.

MAT2114 HOMEWORK 06 3. Let B be a basis for R³ and let v = A (a) Find [v], the coordinate vector of v with respect to the B-basis. [v]B= (b) Suppose T: R3 R2 is the linear transformation satisfying Find T(v). T(b₁)= -1-2 T(ba)= -[2]. T(b)-| - HINT: IN PART (a) YOU FOUND THE COORDINATES OF v. WHAT ARE THOSE COORDINATES ACTUALLY COMMUNICATING TO YOU ABOUT THE RELATIONSHIP BETWEEN V AND B? The 5-43 V₂ 11 2x3-3-1 2+1 T(v) = [13] 10-12-12 2 1476-8 MAT2114 HOMEWORK 06 (c) Find the standard matrix [T] for the transformation 7: R R2 in part (b). NOTE: SIMILAR TO PART (B), DOING THIS WILL REQUIRE YOU TO FIGURE OUT HOW TO WRITE EACH OF THE STANDARD BASIS VECTORS AS LINEAR COMBINATIONS OF THE B-BASIS VECTORS.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 11CM
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Need help with part c
mat2114hw06 MAT2114 HOMEWORK 06 3. Let B= be a basis for R³ and let v = (a) Find [v], the coordinate vector of v with respect to the B-basis. 1002 [v] =\ (b) Suppose T: R3 R2 is the linear transformation satisfying Find T(v). T(b)= T(ba)= = [2]. T(b)= | HINT: IN PART (a) YOU FOUND THE COORDINATES OF v. WHAT ARE THOSE COORDINATES ACTUALLY COMMUNICATING TO YOU ABOUT THE RELATIONSHIP BETWEEN V AND B? The 5-43 -2 2 2x3-3-1 2x1 Va TL 10-12-12 -476-8 T(v) = [13] MAT2114 HOMEWORK 06 (c) Find the standard matrix [T] for the transformation T: R³ → R² in part (b). NOTE: SIMILAR TO PART (B), DOING THIS WILL REQUIRE YOU TO FIGURE OUT HOW TO WRITE EACH OF THE STANDARD BASIS VECTORS AS LINEAR COMBINATIONS OF THE B-BASIS VECTORS. 9:15PM
Transcribed Image Text:mat2114hw06 MAT2114 HOMEWORK 06 3. Let B= be a basis for R³ and let v = (a) Find [v], the coordinate vector of v with respect to the B-basis. 1002 [v] =\ (b) Suppose T: R3 R2 is the linear transformation satisfying Find T(v). T(b)= T(ba)= = [2]. T(b)= | HINT: IN PART (a) YOU FOUND THE COORDINATES OF v. WHAT ARE THOSE COORDINATES ACTUALLY COMMUNICATING TO YOU ABOUT THE RELATIONSHIP BETWEEN V AND B? The 5-43 -2 2 2x3-3-1 2x1 Va TL 10-12-12 -476-8 T(v) = [13] MAT2114 HOMEWORK 06 (c) Find the standard matrix [T] for the transformation T: R³ → R² in part (b). NOTE: SIMILAR TO PART (B), DOING THIS WILL REQUIRE YOU TO FIGURE OUT HOW TO WRITE EACH OF THE STANDARD BASIS VECTORS AS LINEAR COMBINATIONS OF THE B-BASIS VECTORS. 9:15PM
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