If a matrix has 8 elements, what are the possible orders it can h…

Question

If a matrix has 8 elements, what are the possible orders it can have? What if it has 5 elements?

✓

Answer

We know that if a matrix is of order m × n, then it has mn elements.
The possible orders of a matrix with 8 elements are given below:
1 × 8, 2 × 4, 4 × 2, 8 × 1
Thus, there are 4 possible orders of the matrix.
The possible orders of a matrix with 5 elements are given below:
1 × 5, 5 × 1 Thus, there are 2 possible orders of the matrix.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks" from Algebra of Matrices→Algebra of Matrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Evaluate the following integrals:
$\int(\tan\text{x}+\cot\text{x})^2\text{dx}$

→

Find $x$, if $\left[\begin{array}{lll}x & -5 & -1\end{array}\right]\left[\begin{array}{lll}1 & 0 & 2 \\ 0 & 2 & 1 \\ 2 & 0 & 3\end{array}\right]\left[\begin{array}{l}x \\ 4 \\ 1\end{array}\right]=0$

→

Is the binary operation $\ast,$ defined on set N, given by a$a^{\ast}b = \frac{a + b}{2}$ for all $a, b\varepsilon N,$ commutative?
Is the above binary operation $\ast$ associative?

→

Let A = R₀ × R, where R₀ denote the set of all non-zero real numbers. A binary operation '⊙' is defined on A as follows:
(a, b) ⊙ (c, d) = (ac, bc + d) for all (a, b), (c, d) ∈ R₀ × R.
Find the invertible elements in A.

→

Solve the following equation for x:
$3\sin^{-1}\frac{2\text{x}}{1+\text{x}^2}-4\cos^{-1}\frac{1-\text{x}^2}{1+\text{x}^2}+2\tan^{-1}\frac{2\text{x}}{1-\text{x}^2}=\frac{\pi}{3}$

→

If A is square matrix such that A² = A, then show that (I + A)³ = 7A + I.

→

Show that the following point are coplanar:
(0, -1, 0), (2, 1, -1), (1, 1, 1) and (3, 3, 0)

→

Evaluate the following integrals:
$\int_{0}^\limits{1}\text{xe}^{\text{x}^2}\text{ dx}$

→

Discuss the continuity of the following functions at the indicated point:
$\text{f}\text{(x)}=\begin{cases}\text{|x|}\cos\Big(\frac{1}{\text{x}}\Big), & \text{ x}\neq 0\\0 &\text{ x} = 0\end{cases}\text{at x}=0$