If a matrix has 5 elements, write all possible orders it can have.

1.	If a matrix has 5 elements, write all possible orders it can have.
Answer» We are given that, A matrix has 5 elements. We need to find all the possible orders. We know that, If there is a matrix A, of order m × n. Then, There are mn elements. Or, If a matrix has mn elements, then The order of the matrix = m × n or n × m For example, If a matrix is of order 1 × 2, then There are 2 elements in the matrix. [ a₁₁ , a₁₂]_1x2 = 2 elements Or, If a matrix is of order 2 × 1, then There are 2 elements in the matrix. \( \begin{bmatrix}a_{11} \\[0.3em]a_{21}\\[0.3em]\end{bmatrix}_{2\times1}\) = 2 elements Similarly, If a matrix has 5 elements, then The order of this matrix are 1 × 5 or 5 × 1. Thus, Possible orders of a matrix having 5 elements are 1 × 5 and 5 × 1

Answer»

We are given that,

A matrix has 5 elements.

We need to find all the possible orders.

We know that,

If there is a matrix A, of order m × n.

Then,

There are mn elements.

Or,

If a matrix has mn elements, then

The order of the matrix = m × n or n × m

For example,

If a matrix is of order 1 × 2, then

There are 2 elements in the matrix.

[ a₁₁ , a₁₂]_1x2 = 2 elements

Or,

If a matrix is of order 2 × 1, then

There are 2 elements in the matrix.

\( \begin{bmatrix}a_{11} \\[0.3em]a_{21}\\[0.3em]\end{bmatrix}_{2\times1}\) = 2 elements

Similarly,

If a matrix has 5 elements, then

The order of this matrix are 1 × 5 or 5 × 1.

Thus,

Possible orders of a matrix having 5 elements are 1 × 5 and 5 × 1

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