Q.If A=[1−235] and B=[−2354], then find A−4B.
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🔒 Start your 14-day free trial to unlock the full solution →Concept understanding — Matrix Addition
Matrix Addition: The Intuition
You run a fruit stall and record apples and bananas sold each morning and afternoon in a table:
| Time | Apples | Bananas |
|---|---|---|
| Morning | 10 | 5 |
| Afternoon | 8 | 12 |
That's a matrix — a rectangular array of numbers. Your friend's stall has its own table for the same day (morning: 6 apples, 7 bananas; afternoon: 4 apples, 9 bananas). To get the combined sales, you add the numbers in the same position: morning apples with morning apples, afternoon bananas with afternoon bananas, and so on.
That's matrix addition: you add corresponding entries — numbers in the same row and column.
The Precise Statement
(A+B)ij=Aij+Bij
If A and B have the same size (same number of rows and columns), their sum A+B is a matrix of that size where each entry is the sum of the corresponding entries.
Example:
A=[215−3],B=[0742]
A+B=[2+01+75+4−3+2]=[289−1]
The One Rule You Cannot Break
You can only add matrices with the exact same dimensions. A 2×3 matrix cannot be added to a 3×2 matrix — the positions don't match.
Properties That Feel Natural
Matrix addition behaves like ordinary number addition, inheriting these from the addition of individual entries:
- Commutative: A+B=B+A
- Associative: (A+B)+C=A+(B+C)
- Zero matrix: there's a matrix O (all zeros) with A+O=A
A Quick Check …
4B=[−8122016], so A−4B=[1−(−8)−2−123−205−16]=[9−14−17−11]. …
Scale B by 4 entrywise, then subtract entrywise from A.
Step 1 — Compute 4B.
4B=4[−2354]=[4(−2)4(3)4(5)4(4)]=[−8122016].
Step 2 — Compute A−4B.
A−4B=[1−235]−[−8122016]=[1−(−8)−2−123−205−16]=[9−14−17−11].
…
Showing the 12 most recent of 13 on this concept.
- CBSE 2026Set ANNUAL1 markMCQQ.If A=[122331] and B=[3−1−1032], then the (2A−B) will be(a) [−155630](b) [55−1630](c) [244662](d) [−3516−32]
›Reveal solutionSolution
Scale A by 2 and subtract B entry-by-entry.
2A=[244662].
…
- CBSE 2026Set ANNUAL1 markQ.If A = \begin{pmatrix}1 & 2 & 3\ 2 & 3 & 1\end{pmatrix} and B = \begin{pmatrix}3 & -1 & 3\ -1 & 0 & 2\end{pmatrix}, then find the value of 2A - B.
›Reveal solutionSolution
Scale A by 2 (multiply every entry by 2), then subtract B entry-by-entry.
Working:
A=(122331),2A=(244662) …
- CBSE 2024Set ANNUAL1 markMCQQ.If A=[122331] and B=[3−1−1032], then (2A−B) will be:(a) [15−5620](b) [516−503](c) [−155630](d) [−153650]
›Reveal solutionSolution
Scale A by 2 entrywise, then subtract B entrywise.
A=[122331], so 2A=[244662].
B=[3−1−1032].
…
- CBSE 2024Set ANNUAL1 markQ.If A = [[2, 4], [3, 2]], B = [[-2, 5], [3, 4]] then find 3A - B.
›Reveal solutionSolution
Scale A by 3, then subtract B entrywise.
Given A=(2342) and B=(−2354).
3A=(69126)
…
- CBSE 2024Set ANNUAL1 markMCQQ.Let [ILLEGIBLE — page defect obscures the matrix's own name/label] = [[2, 4], [3, 2]], C = [[−2, 5], [3, 4]], the value of [ILLEGIBLE — page defect obscures the operator between the two matrices] C is :(a) [[0, 9], [6, 6]](b) [[0, 6], [?, 6]] — one cell illegible (page defect)(c) [[?, 7], [?, 2]] — two cells illegible (page defect)(d) None of these
›Reveal solutionSolution
Although the matrix's own name/label and the operator symbol between the two matrices are obscured by a scan defect, the arithmetic can be recovered: treating the given matrix and C as being added, the sum matches option (a) exactly.
Note on the source scan: the label of the first matrix (e.g. 'A' or 'B') and the operator between the two matrices are lost to a page-defect blot. Given matrix (unnamed) = [[2, 4], [3, 2]] and C = [[−2, 5], [3, 4]].
…
- CBSE 2024Set ANNUAL1 markMCQQ.If [31−42]+X=[3510], then the matrix X is ............... .(a) [6454](b) [0452](c) [045−2](d) [0−45−2]
›Reveal solutionSolution
Isolate X by subtracting the given matrix from the right-hand side matrix.
Given [31−42]+X=[3510]
…
- CBSE 2023Set ANNUAL1 markQ.If A = [[1, 3], [-2, 5]] and B = [[2, 4], [3, 2]] then find A + B.
›Reveal solutionSolution
Add corresponding entries of the two matrices.
Matrix addition is defined entry-by-entry: if A=[aij] and B=[bij] are matrices of the same order, then A+B=[aij+bij].
Here A=[[1,3],[−2,5]] and B=[[2,4],[3,2]].
…
- CBSE 2022Set ANNUAL1 markMCQQ.If A=[1021] and B=[2−110], then find 2A+3B.(a) [6052](b) [8−372](c) [7−372](d) [8−273]
›Reveal solutionSolution
Scale each matrix entrywise, then add corresponding entries.
A=[1021], B=[2−110].
2A=[2042], 3B=[6−330].
…
- CBSE 2022Set ANNUAL1 markQ.If A=[1−235] and B=[2342], then A−B= ______.
›Reveal solutionSolution
Subtract matrices entry-by-entry.
A=[1−235], B=[2342].
…
- CBSE 2022Set ANNUAL1 markQ.If matrix A=[2342] and B=[−2354], then find the value of 3A−B.
›Reveal solutionSolution
Scale A by 3 entrywise, then subtract B entrywise.
Given A=[2342], B=[−2354].
Step 1: Compute 3A by multiplying every entry by 3:
3A=[69126]
Step 2: Subtract B entrywise (matrices must have the same order to add/subtract, which they do here, both 2×2): …
- CBSE 2021Set I1 markMCQQ.[1001]+[0110]=(a) [2002](b) [0220](c) [2222](d) [1111]
›Reveal solutionSolution
Matrix addition is component-wise.
Add corresponding entries:
…
- CBSE 2020Set ANNUAL1 markQ.If A = [[1, 3], [−2, 5]] and B = [[−2, 5], [3, 4]], find the value of A − B.
›Reveal solutionSolution
Subtract corresponding entries of the two matrices.
…
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