Question

Total number of possible matrices of order 2 × 3 with each entry 1 or 0 is 





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Answer 1

Answer:

The given matrix of the order 3×3 ha 9 elements and each of these elements can be either 0 or 1. Now, each of the 9 elements can be chosen in two possible ways. Therefore, by the multiplication principle, the required number of possible matrices is 29=512.

Answer 2

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

$\red{ \textsf{The number of all possible matrices of order 2x3 with entry 1 or 0 are 64 .}}$

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

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

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

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

$\orange{ \textsf{Having entries 1 and 0 .}}$

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

$\red{ \textsf{a11 can have two entries 1 and 0 .}} \\ \red{ \textsf{a12 can have two entries 1 and 0 .}} \\ \red{ \textsf{a13 can have two entries 1 and 0 .}} \\ \red{ \textsf{a21 can have two entries 1 and 0 .}} \\ \red{ \textsf{a22 can have two entries 1 and 0 .}} \\ \red{ \textsf{a23 can have two entries 1 and 0 .}}$

$\red{ \textsf{Therefore , The number of all possible matrices of order 2 x 3 with entry 1 or 0 are :}}$

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

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

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

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

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

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 .