CBSE Sample Paper 2020-21 · Part A: Section I · 1 mark

Q4: Order of $5A - 3B$ for $A_{3 \times n}$ and $B_{m \times 5}$

Sample 2020-21Ch 3 · Matrices

The question

If A and B are matrices of order $3 \times n$ and $m \times 5$ respectively, then find the order of matrix $5A - 3B$ ⁠, given that it is defined.

Exam answer

$5A$ has the order of A, $3 \times n$ ⁠, and $3B$ has the order of B, $m \times 5$ ⁠.

Why?

Multiplying a matrix by a number multiplies every entry by that number. The number of rows and columns does not change.

$5A - 3B$ is defined only when A and B have the same order.

Why?

Matrices are subtracted entry by entry, so every entry of $5A$ needs a partner in the same place in $3B$ ⁠. That needs the same number of rows and the same number of columns.

3 \times n = m \times 5 \Rightarrow m = 3,\ n = 5

Why?

Compare the rows: $3 = m$ ⁠. Compare the columns: $n = 5$ ⁠. The answer has the same order as A and B.

$\therefore$ the order of $5A - 3B$ is $3 \times 5$ ⁠.

Where this comes from

Chapter 3, Matrices: Order of a matrix; addition of matrices.

Question type: One-mark MCQs

How to spot it: click to see

Type 6. One-mark MCQs: orders and definitions

Spot it: four options, asking when a sum or product is defined, what order it has, or what a word such as symmetric or inverse means.

Here: $5A - 3B$ is a difference, so $A$ and $B$ need the same order: $3 \times n = m \times 5$ gives $m = 3$ ⁠, $n = 5$ ⁠, and the answer is $3 \times 5$ ⁠.

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Matrices in past papers: question 23 of 24 · see them all

Q4: Order of 5A−3B5A - 3B5A−3B for A3×nA_{3 \times n}A3×n​ and Bm×5B_{m \times 5}Bm×5​

Q4: Order of $5A - 3B$ for $A_{3 \times n}$ and $B_{m \times 5}$