Allied & ICAR Exam Bank • ALLIED_2613 MCQ • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Linear and orthogonal transformations

Question Statement:

Under a linear transformation $T(x) = A x$, the zero vector is mapped to:

Options:

  • (A) The zero vector
  • (B) An arbitrary unit vector
  • (C) Undefined
  • (D) Vector with all entries equal to 1

Answer Key:

A

Step-by-Step Solution & Explanation

Every linear map preserves the origin: $T(0) = T(0 \cdot v) = 0 \cdot T(v) = 0$.
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