3. A linear transformation from R4 to R³ is given by it's action on the standard basis vectors of R4 via: 1 (a) Write down the matrix representing this linear transformation in this basis. (b) By direct application of the matrix multiplication, find the action of this linear trans- formation on the vector: 2 3 -1 (c) Verify that you get the same vector if you apply the linear transformation on each basis vector, and use linearity of the transformation, in the expansion of the above vector , 1 0 으ㅇ

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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3. A linear transformation from R4 to R³ is given by it's action on the standard basis vectors
of R4 via:
1
(a) Write down the matrix representing this linear transformation in this basis.
(b) By direct application of the matrix multiplication, find the action of this linear trans-
formation on the vector:
2
3
-1
2
(c) Verify that you get the same vector if you apply the linear transformation on each basis
vector, and use linearity of the transformation, in the expansion of the above vector
as"
2
1
3
= 2
-1
1
+3
1
1
2
(d) Find the kernel of this linear transformation.
Transcribed Image Text:3. A linear transformation from R4 to R³ is given by it's action on the standard basis vectors of R4 via: 1 (a) Write down the matrix representing this linear transformation in this basis. (b) By direct application of the matrix multiplication, find the action of this linear trans- formation on the vector: 2 3 -1 2 (c) Verify that you get the same vector if you apply the linear transformation on each basis vector, and use linearity of the transformation, in the expansion of the above vector as" 2 1 3 = 2 -1 1 +3 1 1 2 (d) Find the kernel of this linear transformation.
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