If A is 3×4 matrix and B is a matrix such that A'B and BA' are both defin

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3 and 4 .Determinants and Matrices

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If $A$ is $3×4$ matrix and $ B$ is a matrix such that $A'B$ and $BA'$ are both defined. Then $B $ is of the type

A

$3 × 4$

B

$3 × 3$

C

$4 × 4$

D

$4 × 3$

Solution

(a) ${A_{3 \times 4}} \Rightarrow {A'_{4 \times 3}}$; Now $A'B$ defined

$ \Rightarrow $ $B$ is $3 \times p$

Again ${B_{3 \times p}}{A'_{4 \times 3}}$ defined

$ \Rightarrow $ $p = 4$

$\therefore $ $B$ is $3 \times 4$.

Standard 12

Mathematics

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