Question

write the number of all possible matrices of order 2×3 with each entry 1 or 2​

Answer 1

Answer

Order is 2×3

Number of elements = 6

in which 1,2, (Two) entry can be filled

and can repeat.

Number of possible matrices = 2^6=64

Answer 2

$\huge \purple{ \underline{ \boxed{ \red{ \mathbb{ANSWER : }}}}}$

$\red{ \textsf{The number of all possible matrices of order 2x3 with entry 1 or 2 are 64 .}}$

$\huge \purple{ \underline{ \boxed{ \red{ \mathbb{EXPLANATION : }}}}}$

$\large \green{ \underline{ \underline{ \mathbb{GIVEN : }}}}$

$\orange{ \textsf{A matrix with order 2 x 3 :}}$

$\orange{\left[ \begin{array}{c c c} \bf{a11}&\bf{a12}& \bf{a13} \\ \bf{a21}&\bf{a22}&\bf{a23} \end{array}\right]}$

$\orange{ \textsf{Having entries 1 and 2 .}}$

$\large \green{ \underline{ \underline{ \mathbb{SOLUTION : }}}}$

$\red{ \textsf{a11 can have two entries 1 and 2 .}} \\ \red{ \textsf{a12 can have two entries 1 and 2 .}} \\ \red{ \textsf{a13 can have two entries 1 and 2 .}} \\ \red{ \textsf{a21 can have two entries 1 and 2 .}} \\ \red{ \textsf{a22 can have two entries 1 and 2 .}} \\ \red{ \textsf{a23 can have two entries 1 and 2 .}}$

$\red{ \textsf{Therefore , The number of all possible matrices of order 2 x 3 with entry 1 or 2 are :}}$

$\red{ \longrightarrow{ \mathbb{2 \times 2 \times 2 \times 2 \times 2 \times 2}}}$

$\red{ \longrightarrow{ \mathbb{ {2}^{6} }}}$

$\red{ \longrightarrow{ \mathbb{64}}}$

$\large \green{ \underline{ \underline{ \mathbb{KNOW \: MORE : }}}}$

$\orange{\mathbb{MATRIX : }}$

A matrix is an rectangular array having 'm' number of rows and 'n' number of columns .

$\orange{ \mathbb{ORDER \: OF \: MATRIX :}}$

A matrix having 'm' number of rows and 'n' number of columns is said to be matrix of order m x n .