I) If A E Mat4,3(R), call TA : R R the linear operator whose matrix in the standard bases of R3 and R' is A. For which one of these values of A is TA injective. 1 a) A = 3 10 1 0. 0. b) A = 0. 1 c) A = -2 2 2 122 12 2

I) If A E Mat4,3(R), call TA : R R the linear operator whose matrix in the standard bases of R3 and R' is A. For which one of these values of A is TA injective. 1 a) A = 3 10 1 0. 0. b) A = 0. 1 c) A = -2 2 2 122 12 2

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

I) If A E Mat4,3 (R), call TA : R R the linear operator whose matrix in the
standard bases of R3 and R is A. For which one of these values of A is TA injective.
2 1
a) A =
3.
0.
1
0.
0 0
0.
b) A =
1.
0.
1.
c) A =
21
21
2
2

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