MathematicsChapter 2: Matrices and Determinants
Add and Subtract
(A+B)_{ij} = a_{ij}+b_{ij}.
Learning objectives
- State the rule or meaning of add and subtract in easy words.
- Apply add and subtract in a clear step-by-step solution.
- Check the conditions, working, and final answer for accuracy.
Definition
(A+B)ij = aij+bij. Commutative: A+B=B+A. Associative: (A+B)+C=A+(B+C). A+O=A.
Mathematical form
B=B+A. Associative
C=A+(B+C). A+O
Where / symbols
- ADD AND SUBTRACT
- (A+B)_{ij} = a_{ij}+b_{ij}. Commutative: A+B=B+A. Associative: (A+B)+C=A+(B+C). A+O=A.
- ADD AND SUBTRACT
- (A+B)_{ij} = a_{ij}+b_{ij}.
Overview
Understand the idea, then apply it:
Main Idea
(A+B)ij = aij+bij. Commutative: A+B=B+A. Associative: (A+B)+C=A+(B+C). A+O=A.
Examples [[1,2]]+[[3,4]]=[[4,6]] · Sizes must match · Subtract: minus each pair
Exam Use
Write the rule first: (A+B)ij = a{ij}+b_{ij}. 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 — ADD AND SUBTRACT
(A+B)ij = aij+bij. Commutative: A+B=B+A. Associative: (A+B)+C=A+(B+C). A+O=A.
WHY — Why it matters
This rule is a separate learning unit inside addition and scalar multiply. It can be defined, applied, and checked in its own FBISE question.
HOW — How to answer
Write the rule first: (A+B)ij = a{ij}+b_{ij}. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
How to answer a add and subtract 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
Do not add a 2x2 to a 2x3. Check size before you start.
Key points
- entrywise
- same size to add
- kA multiplies every entry
- focused answer
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Add and Subtract
Sticky Notes · Quick Revision
Core Idea
- (A+B)ij = aij+bij.
What to Know
- (A+B)ij = aij+bij. Commutative: A+B=B+A. Associative: (A+B)+C=A+(B+C). A+O=A.
Example or Evidence
- [[1,2]]+[[3,4]]=[[4,6]]
- Sizes must match
- Subtract: minus each pair
How to Answer
- Write the rule first: (A+B)ij = a{ij}+b_{ij}. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Common Error
- Do not add a 2x2 to a 2x3. Check size before you start.
FBISE Exam Check
- State the rule, show the working, and check the answer.
60-second revision
- (A+B)ij = aij+bij.
- [[1,2]]+[[3,4]]=[[4,6]]
- Sizes must match
- State the rule, show the working, and check the answer.
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