If oA-2- 3- oB-3- 2- oC-3- 3- then which of the following is undefined

Explanation for the correct optionOption(D): Order of a matrix P is given by o(P)=(number of rows)×(number of columns) and the order of transpose of matrix P is ...

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Byju's Answer

Standard XII

Mathematics

Multiplication of Matrices

If oA=2× 3, o...

Question

If $o (A) = 2 \times 3, o (B) = 3 \times 2, o (C) = 3 \times 3$ , then which of the following is undefined

$C B + A'$

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$B A C$

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$C (A + B')'$

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$C (A + B')$

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Solution

The correct option is D
$C (A + B')$

Explanation for the correct option
Option(D): Order of a matrix $P$ is given by $o (P) =$ (number of rows) $\times$ (number of columns) and the order of transpose of matrix $P$ is given as
$o (P') =$ (number of columns) $\times$ (number of rows)
Given that $o (A) = 2 \times 3, o (B) = 3 \times 2, o (C) = 3 \times 3$
$\begin{matrix} ∴ & o (A) & = & 2 \times 3 \\ o (B') & = & 2 \times 3 \end{matrix}$
Two matrices can be added only if they are of same order
$∴$ Matrices $A$ and $B'$ can be added and $o (A + B') = 2 \times 3$
To perform matrix multiplication the number of columns of first matrix must be equal to number of rows of second matrix
Here number of columns of matrix $C$ i.e. $3$ $\neq$ number of rows of matrix $(A + B')$ i.e. $2$
Hence, $C (A + B')$ is undefined
Hence, option(D) is correct
Explanation for incorrect options
Option(A): $o (C) = 3 \times 3, o (B) = 3 \times 2, o (A) = 2 \times 3$
$\Rightarrow o (C B) = 3 \times 2$ and $o (A') = 3 \times 2$
$∴ C B + A'$ is defined
Option(B): $o (C) = 3 \times 3, o (A) = 2 \times 3$ $\Rightarrow o (A C) = 2 \times 3$
$o (B) = 3 \times 2$ and $o (A C) = 2 \times 3$
$∴ B A C$ is defined
Option(C): $o (A) = 2 \times 3, o (B) = 3 \times 2, o (C) = 3 \times 3$
$\Rightarrow o (B') = 2 \times 3$ and $o (A + B') = 2 \times 3$
$\Rightarrow o (A + B')' = 3 \times 2$
$∴ C (A + B')'$ is defined
Hence options (A), (B) and (C) are incorrect
Hence, the correct option is option(D) i.e. $C (A + B')$

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If oA=2×3,oB=3×2,oC=3×3, then which of the following is undefined

If $o (A) = 2 \times 3, o (B) = 3 \times 2, o (C) = 3 \times 3$ , then which of the following is undefined