Math Problem Statement

answer all in one word Suppose TA(x)=Ax is a linear transform.

If there is at least one vector in the co-domain of TA(x) that is not in the range of the transform, then TA(x) cannot be one-to-one.

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Linear Transformations
Co-domain
Range

Formulas

T_A(x) = Ax

Theorems

Rank-Nullity Theorem
Injectivity Criterion

Suitable Grade Level

College Level

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