MathematicsChapter 2: Matrices and Determinants
DETERMINANT OF A 2x2 MATRIX
ad-bc. Swapping two rows changes sign.
Learning objectives
- State the rule or meaning of determinant of a 2x2 matrix in easy words.
- Apply determinant of a 2x2 matrix in a clear step-by-step solution.
- Check the conditions, working, and final answer for accuracy.
Definition
ad-bc. Swapping two rows changes sign. If two rows equal, det=0. det(kA)=k^n det A for n x n.
Formula
det=0. det(kA)
Where / symbols
- DETERMINANT OF A 2x2 MATRIX
- ad-bc. Swapping two rows changes sign. If two rows equal, det=0. det(kA)=k^n det A for n x n.
- 2x2
- ad-bc.
Overview
Understand the idea, then apply it:
Main Idea
ad-bc. Swapping two rows changes sign. If two rows equal, det=0. det(kA)=k^n det A for n x n.
Examples [[1,2],[3,4]] -> -2 · Singular if det=0 · det A^T = det A
Exam Use
Write the rule first: ad-bc. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Examples State the central idea · Use one accurate detail · Check the final response
WHAT — DETERMINANT OF A 2x2 MATRIX
ad-bc. Swapping two rows changes sign. If two rows equal, det=0. det(kA)=k^n det A for n x n.
WHY — Why it matters
This rule is a separate learning unit inside determinants 2x2 and 3x3. It can be defined, applied, and checked in its own FBISE question.
HOW — How to answer
Write the rule first: ad-bc. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
How to answer a determinant of a 2x2 matrix question
- Read the exact command word and identify what the question asks.
- State the matching idea, rule, or meaning before adding detail.
- Use the unit evidence or mathematical working that directly supports the answer.
- Check accuracy, relevance, and answer length before finishing.
In simple words
The sign is (-1)i+j, not 'always plus'. Chessboard of + and -.
Key points
- ad minus bc
- 2x2: ad-bc
- 3x3: cofactor expansion
- focused answer
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.DETERMINANT OF A 2x2 MATRIX
Sticky Notes · Quick Revision
Core Idea
- ad-bc.
What to Know
- ad-bc. Swapping two rows changes sign. If two rows equal, det=0. det(kA)=k^n det A for n x n.
Example or Evidence
- [[1,2],[3,4]] -> -2
- Singular if det=0
- det AT = det A
How to Answer
- Write the rule first: ad-bc. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Common Error
- The sign is (-1)i+j, not 'always plus'. Chessboard of + and -.
FBISE Exam Check
- State the rule, show the working, and check the answer.
60-second revision
- ad-bc.
- [[1,2],[3,4]] -> -2
- Singular if det=0
- State the rule, show the working, and check the answer.
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