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Addition and Scalar Multiply
Add (or subtract) entrywise, only if the sizes match. Scalar k times A multiplies every entry by k. Negative: -A = (-1)A. Meaning: addition is 'same box, add matching numbers'. It is not matrix multiplication (next page).
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Addition and Scalar Multiply
What is it?
Add (or subtract) entrywise, only if the sizes match. Scalar k times A multiplies every entry by k. Negative: -A = (-1)A. Meaning: addition is 'same box, add matching numbers'. It is not matrix multiplication (next page).
In simple words
- Add (or subtract) entrywise, only if the sizes match.
- Scalar k times A multiplies every entry by k.
- Negative: -A = (-1)A.
- Do not add a 2x2 to a 2x3. Check size before you start.
Important terms
ADDITION AND SCALAR MULTIPLY: Add (or subtract) entrywise, only if the sizes match. Scalar k times A multiplies every entry by k. Negative: -A = (-1)A. Meaning: addition is 'same box, add matching numbers'. It is not matrix multiplication (next page).
1. ADD AND SUBTRACT: (A+B)ij = aij+bij. Commutative: A+B=B+A. Associative: (A+B)+C=A+(B+C). A+O=A.
2. SCALAR: 2A doubles every number. (k+m)A = kA+mA. k(A+B)=kA+kB. Complex scalar: same rule, using complex arithmetic on each entry.
What you should learn
- State the main ideas and notation used in addition and scalar multiply.
- Apply the rules of addition and scalar multiply in a clear, step-by-step solution.
- Check signs, conditions, and the final answer for mathematical accuracy.
Examples
- [[1,2]]+[[3,4]]=[[4,6]]
- Sizes must match
- Subtract: minus each pair
ADD AND SUBTRACT
(A+B)ij = aij+bij. Commutative: A+B=B+A. Associative: (A+B)+C=A+(B+C). A+O=A.
SCALAR
2A doubles every number. (k+m)A = kA+mA. k(A+B)=kA+kB. Complex scalar: same rule, using complex arithmetic on each entry.
Recommended for Class 11
Full school-level explanation
Add (or subtract) entrywise, only if the sizes match. Scalar k times A multiplies every entry by k. Negative: -A = (-1)A. Meaning: addition is 'same box, add matching numbers'. It is not matrix multiplication (next page).
Add matching boxes:
WHAT — ADDITION AND SCALAR MULTIPLY
Add (or subtract) entrywise, only if the sizes match. Scalar k times A multiplies every entry by k. Negative: -A = (-1)A. Meaning: addition is 'same box, add matching numbers'. It is not matrix multiplication (next page).
RULE — 1. ADD AND SUBTRACT
(A+B)ij = aij+bij. Commutative: A+B=B+A. Associative: (A+B)+C=A+(B+C). A+O=A.
METHOD — 2. SCALAR
2A doubles every number. (k+m)A = kA+mA. k(A+B)=kA+kB. Complex scalar: same rule, using complex arithmetic on each entry.
WORKED EXAMPLE
Worked: 2[[1, -i],[0, 3]] - [[1, i],[2, 1]]. 2A = [[2, -2i],[0, 6]] minus B: [[2-1, -2i-i],[0-2, 6-1]] = [[1, -3i],[-2, 5]]
ADD AND SUBTRACT
(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
SCALAR
2A doubles every number. (k+m)A = kA+mA. k(A+B)=kA+kB. Complex scalar: same rule, using complex arithmetic on each entry.
Remember
- every entry
Examples
- -A flips signs
- 0 A = O
- Distributive
How to answer a addition and scalar multiply question
How it works
- Identify the given quantities, notation, and required result.
- Choose the matching rule and write it before substitution.
- Work one algebraic step at a time, keeping brackets and signs clear.
- Check restrictions, simplify the result, and verify it where possible.
Remember
- same size to add
- kA multiplies every entry
- [[1,-3i],[-2,5]]
- size first
- entrywise
- every entry
- same size to add
- kA multiplies every entry
How the ideas connect
Worked: 2[[1, -i],[0, 3]] - [[1, i],[2, 1]]. 2A = [[2, -2i],[0, 6]] minus B: [[2-1, -2i-i],[0-2, 6-1]] = [[1, -3i],[-2, 5]]
Deeper understanding
Go beyond memorising Addition and Scalar Multiply. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Worked: 2[[1, -i],[0, 3]] - [[1, i],[2, 1]]. 2A = [[2, -2i],[0, 6]] minus B: [[2-1, -2i-i],[0-2, 6-1]] = [[1, -3i],[-2, 5]]
Common mistakes
Exam focus
Core Idea
1. ADD AND SUBTRACT
2. SCALAR
Worked Example
Exam focus
Quick revision
- same size to add
- kA multiplies every entry
- [[1,-3i],[-2,5]]
- size first
- ADDITION AND SCALAR MULTIPLY: Add (or subtract) entrywise, only if the sizes match. Scalar k times A multiplies every entry by k.
- 1. ADD AND SUBTRACT: (A+B)ij = aij+bij. Commutative: A+B=B+A. Associative: (A+B)+C=A+(B+C). A+O=A.
Do not add a 2x2 to a 2x3. Check size before you start.
For long answers on Addition and Scalar Multiply: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- same size to add
- kA multiplies every entry
- [[1,-3i],[-2,5]]
- size first
Important formulas
- same size to add
- kA multiplies every entry
- [[1,-3i],[-2,5]]
Common exam traps
- Do not add a 2x2 to a 2x3. Check size before you start.
- Do not use a remembered 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 use a remembered formula before checking that its conditions fit the question.
- Mistake
Do not hide sign changes or restrictions; write them on the line where they are used.
- 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.
same size to add
kA multiplies every entry
[[1,-3i],[-2,5]]
size first
Add (or subtract) entrywise, only if the sizes match. Scalar k times A multiplies every entry by k. Negative: -A = (-1)A. Meaning: addition is 'same box, add ma
- Definition
- Add (or subtract) entrywise, only if the sizes match. Scalar k times A multiplies every entry by k. Negative: -A = (-1)A. Meaning: addition is 'same box, add ma
- 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 Addition and Scalar Multiply.
Explain
Q2. Explain: ADD AND SUBTRACT.
Example
Q3. Give one clear example of Addition and Scalar Multiply and say why it fits.
Mistake
Q4. State one common mistake students make about Addition and Scalar Multiply.
Exam note
Q5. Write a short exam note on Addition and Scalar Multiply: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.