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Add and Subtract
(A+B)ij = aij+bij. Commutative: A+B=B+A. Associative: (A+B)+C=A+(B+C). A+O=A.
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Add and Subtract
What is it?
(A+B)ij = aij+bij. Commutative: A+B=B+A. Associative: (A+B)+C=A+(B+C). A+O=A.
In simple words
- (A+B)ij = aij+bij.
- [[1,2]]+[[3,4]]=[[4,6]]
- Sizes must match
- State the rule, show the working, and check the answer.
Important terms
ADD AND SUBTRACT: (A+B)ij = aij+bij. Commutative: A+B=B+A. Associative: (A+B)+C=A+(B+C). A+O=A.
ADD AND SUBTRACT: (A+B)ij = aij+bij.
What you should learn
- 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.
Examples
- [[1,2]]+[[3,4]]=[[4,6]]
- Sizes must match
- Subtract: minus each pair
MAIN IDEA
(A+B)ij = aij+bij. Commutative: A+B=B+A. Associative: (A+B)+C=A+(B+C). A+O=A.
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.
Recommended for Class 11
Full school-level explanation
(A+B)ij = aij+bij. Commutative: A+B=B+A. Associative: (A+B)+C=A+(B+C). A+O=A.
Understand the idea, then apply it:
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.
MAIN IDEA
(A+B)ij = aij+bij. Commutative: A+B=B+A. Associative: (A+B)+C=A+(B+C). A+O=A.
Remember
- entrywise
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.
Remember
- focused answer
- accurate support
Examples
- State the central idea
- Use one accurate detail
- Check the final response
How to answer a add and subtract question
How it works
- 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.
Remember
- entrywise
- same size to add
- kA multiplies every entry
- size first
- entrywise
- focused answer
- accurate support
- entrywise
Deeper understanding
Go beyond memorising Add and Subtract. Connect the definition to reasons, relationships, exceptions, and exam wording.
Common mistakes
Exam focus
Core Idea
What to Know
Example or Evidence
How to Answer
Exam focus
Quick revision
- entrywise
- same size to add
- kA multiplies every entry
- size first
- ADD AND SUBTRACT: (A+B)ij = aij+bij. Commutative: A+B=B+A. Associative: (A+B)+C=A+(B+C). A+O=A.
- ADD AND SUBTRACT: (A+B)ij = aij+bij.
Do not add a 2x2 to a 2x3. Check size before you start.
For long answers on Add and Subtract: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- entrywise
- same size to add
- kA multiplies every entry
- size first
Important formulas
- entrywise
- same size to add
- kA multiplies every entry
Common exam traps
- Do not add a 2x2 to a 2x3. Check size before you start.
- Do not choose a formula before checking that its conditions fit the question.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Do not add a 2x2 to a 2x3. Check size before you start.
- Mistake
Do not choose a formula before checking that its conditions fit the question.
- Mistake
Do not hide sign changes, restrictions, or skipped algebra steps.
- Mistake
Do not add a 2x2 to a 2x3. Check size before you start.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
entrywise
same size to add
kA multiplies every entry
size first
(A+B)ij = aij+bij. Commutative: A+B=B+A. Associative: (A+B)+C=A+(B+C). A+O=A.
- Definition
- (A+B)ij = aij+bij. Commutative: A+B=B+A. Associative: (A+B)+C=A+(B+C). A+O=A.
- Example
- [[1,2]]+[[3,4]]=[[4,6]]
- Critical warning
- Do not add a 2x2 to a 2x3. Check size before you start.
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Exam Practice
Define
Q1. Define Add and Subtract.
Explain
Q2. Explain: MAIN IDEA.
Example
Q3. Give one clear example of Add and Subtract and say why it fits.
Mistake
Q4. State one common mistake students make about Add and Subtract.
Exam note
Q5. Write a short exam note on Add and Subtract: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.