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Matrices & Determinants
Mathematics
Useful for: UPSC NDA/NA
Overview
Matrices organise numbers in rows and columns; determinants of square matrices tell whether inverses exist and solve linear systems.
Key points
- A matrix of order m × n has m rows and n columns.
- Matrix multiplication is generally not commutative (AB ≠ BA).
- For a 2 × 2 matrix [[a, b], [c, d]], determinant = ad − bc.
- A matrix has an inverse only if its determinant is non-zero.
- Transpose swaps rows and columns; a symmetric matrix equals its transpose.
- Cramer’s rule solves linear systems using determinants.
Practice MCQs
From the perspective of definition and scope, which one of the following statements about Matrices & Determinants is correct?
- Do not apply a memorized Matrices & Determinants formula without checking its conditions.
- Matrices & Determinants is unrelated to institutions, processes or real-world applications.
- Matrices & Determinants has no exceptions or limitations in exam analysis.
- Matrices & Determinants questions reward a formula-first approach and accurate algebraic manipulation.
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Answer: (d) Matrices & Determinants questions reward a formula-first approach and accurate algebraic manipulation.. Matrices & Determinants questions reward a formula-first approach and accurate algebraic manipulation.
Consider the following statements on Matrices & Determinants, focusing on definition and scope: 1. Matrices & Determinants questions reward a formula-first approach and accurate algebraic manipulation. 2. Do not apply a memorized Matrices & Determinants formula without checking its conditions. Which of the statements given above is/are correct?
- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2
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Answer: (a) 1 only. Statement 1 is correct; Statement 2 is a common misconception.
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