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Addition, Subtraction, Scalar
Add or subtract only when both matrices have the same order: combine matching entries. Scalar kA multiplies every entry by k. -A is (-1)A. These operations are entry-wise, not row-dot-column (that is multiplication).
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Addition, Subtraction, Scalar
What is it?
Add or subtract only when both matrices have the same order: combine matching entries. Scalar kA multiplies every entry by k. -A is (-1)A. These operations are entry-wise, not row-dot-column (that is multiplication).
In simple words
- Add or subtract only when both matrices have the same order: combine matching entries.
- ADD AND SUBTRACT: [[1,2],[3,4]] + [[5,6],[7,8]] = [[6,8],[10,12]].
- SCALAR: 3[[1,4],[2,-1]] = [[3,12],[6,-3]].
- Worked-method reminder: kA = [[3, 12], [6, -3]]
Important terms
ADDITION, SUBTRACTION, SCALAR: Add or subtract only when both matrices have the same order: combine matching entries. Scalar kA multiplies every entry by k. -A is (-1)A. These operations are entry-wise, not row-dot-column (that is multiplication).
ADD AND SUBTRACT: [[1,2],[3,4]] + [[5,6],[7,8]] = [[6,8],[10,12]]. Subtract matching entries. 4-(-4)=8 when a minus meets a minus.
SCALAR: 3[[1,4],[2,-1]] = [[3,12],[6,-3]]. k=-1 flips every sign. This is not the determinant and not the inverse.
What you should learn
- Explain addition, subtraction, scalar using the correct definitions, conditions, and notation.
- Apply same order to add, k multiplies every entry correctly in routine and exam-style questions.
- Show each important step, simplify the result, and check that it satisfies the original conditions.
Examples
- 1+5=6
- 4-(-4)=8
- Different orders: cannot add
ADD AND SUBTRACT
[[1,2],[3,4]] + [[5,6],[7,8]] = [[6,8],[10,12]]. Subtract matching entries. 4-(-4)=8 when a minus meets a minus.
SCALAR
3[[1,4],[2,-1]] = [[3,12],[6,-3]]. k=-1 flips every sign. This is not the determinant and not the inverse.
Recommended for Class 10
Full school-level explanation
Add or subtract only when both matrices have the same order: combine matching entries. Scalar kA multiplies every entry by k. -A is (-1)A. These operations are entry-wise, not row-dot-column (that is multiplication).
Same shape, then entry by entry:
WHAT — ADDITION, SUBTRACTION, SCALAR
Add or subtract only when both matrices have the same order: combine matching entries. Scalar kA multiplies every entry by k. -A is (-1)A. These operations are entry-wise, not row-dot-column (that is multiplication). The symbols and conditions are part of the mathematics, so include them when stating the rule.
WHY — Why this topic matters
Addition, Subtraction, Scalar matters because matrices organise numbers and give short methods for transformations and simultaneous equations. Correct order, determinant, and multiplication rules prevent most exam errors.
HOW — How to solve and explain it
Start by identifying what is given and what must be found. Work through ADD AND SUBTRACT, then SCALAR. Worked: A = [[9, -1], [4, 2]], B = [[3, 5], [-4, 6]]. Find A - B. A - B = [[9-3, -1-5], [4-(-4), 2-6]] = [[6, -6], [8, -4]] Worked: k = 3, A = [[1, 4], [2, -1]]. Find kA. kA = [[3, 12], [6, -3]] Finish by checking signs, restrictions, units, and whether the answer matches the question.
ADD AND SUBTRACT
[[1,2],[3,4]] + [[5,6],[7,8]] = [[6,8],[10,12]]. Subtract matching entries. 4-(-4)=8 when a minus meets a minus.
Remember
- matching positions
Examples
- 1+5=6
- 4-(-4)=8
- Different orders: cannot add
SCALAR
3[[1,4],[2,-1]] = [[3,12],[6,-3]]. k=-1 flips every sign. This is not the determinant and not the inverse.
Remember
- every entry times k
Examples
- 3A scales all
- -A negates all
- Not AB
Remember
- same order to add
- k multiplies every entry
- [[6,-6],[8,-4]]
- [[3,12],[6,-3]]
- same order
- matching positions
- every entry times k
- same order to add
How the ideas connect
Worked: A = [[9, -1], [4, 2]], B = [[3, 5], [-4, 6]]. Find A - B. A - B = [[9-3, -1-5], [4-(-4), 2-6]] = [[6, -6], [8, -4]] Worked: k = 3, A = [[1, 4], [2, -1]]. Find kA. kA = [[3, 12], [6, -3]]
Deeper understanding
Go beyond memorising Addition, Subtraction, Scalar. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Worked: A = [[9, -1], [4, 2]], B = [[3, 5], [-4, 6]]. Find A - B. A - B = [[9-3, -1-5], [4-(-4), 2-6]] = [[6, -6], [8, -4]] Worked: k = 3, A = [[1, 4], [2, -1]]. Find kA. kA = [[3, 12], [6, -3]]
Common mistakes
Exam focus
Core Idea
ADD AND SUBTRACT
SCALAR
Worked Method
Exam focus
Quick revision
- same order to add
- k multiplies every entry
- [[6,-6],[8,-4]]
- [[3,12],[6,-3]]
- ADDITION, SUBTRACTION, SCALAR: Add or subtract only when both matrices have the same order: combine matching entries. Scalar kA mul
- ADD AND SUBTRACT: [[1,2],[3,4]] + [[5,6],[7,8]] = [[6,8],[10,12]]. Subtract matching entries. 4-(-4)=8 when a minus me
You cannot add a 2x3 to a 3x2. Same number of entries is not enough; the order must match.
For long answers on Addition, Subtraction, Scalar: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- same order to add
- k multiplies every entry
- [[6,-6],[8,-4]]
- [[3,12],[6,-3]]
Important formulas
- same order to add
- k multiplies every entry
- [[6,-6],[8,-4]]
Common exam traps
- You cannot add a 2x3 to a 3x2. Same number of entries is not enough; the order must match.
- Different orders: cannot add
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
You cannot add a 2x3 to a 3x2. Same number of entries is not enough; the order must match.
- Mistake
Different orders: cannot add
- Mistake
Not AB
- Mistake
Do not treat ADD AND SUBTRACT and SCALAR as the same step; each has a different purpose.
- Mistake
You cannot add a 2x3 to a 3x2. Same number of entries is not enough; the order must match.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
same order to add
k multiplies every entry
[[6,-6],[8,-4]]
[[3,12],[6,-3]]
Add or subtract only when both matrices have the same order: combine matching entries. Scalar kA multiplies every entry by k. -A is (-1)A. These operations are
- Definition
- Add or subtract only when both matrices have the same order: combine matching entries. Scalar kA multiplies every entry by k. -A is (-1)A. These operations are
- Example
- 1+5=6
- Critical warning
- You cannot add a 2x3 to a 3x2. Same number of entries is not enough; the order must match.
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Exam Practice
Define
Q1. Define Addition, Subtraction, Scalar.
Explain
Q2. Explain: ADD AND SUBTRACT.
Example
Q3. Give one clear example of Addition, Subtraction, Scalar and say why it fits.
Mistake
Q4. State one common mistake students make about Addition, Subtraction, Scalar.
Exam note
Q5. Write a short exam note on Addition, Subtraction, Scalar: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.