First slide

Introduction to matrices

Question

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

Moderate

A

$3 \times 4$
B

$3 \times 3$
C

$4 \times 4$
D

$4 \times 3$

Solution

Let the order of B be m $\times$ n.
Since A is 3 $\times$ 4 matrix,
$∴$ A′ is 4 $\times$ 3 matrix.
Since A′ B is defined,
$∴$ number of columns of A′ must be equal to number of rows of B,
$∴$ m = 3.
Also, since BA′ is defined,
$∴$ number of columns of B must be equal to number of rows of A′,
$∴$ n = 4.
$∴$ B is 3 $\times$ 4 matrix

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