In an upper triangular matrix of order n time | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) An upper triangular matrix $A = [a_{ij}]$ is a square matrix where all elements below the main diagonal are zero,i.e.,$a_{ij} = 0$ for all $i > j$

Vedclass · Accepted Answer

$n(n - 1)/2$

Vedclass · Answer

(A) An upper triangular matrix $A = [a_{ij}]$ is a square matrix where all elements below the main diagonal are zero,i.e.,$a_{ij} = 0$ for all $i > j$.For an $n 	imes n$ matrix,the number of elements below the main diagonal is given by the sum of the first $(n-1)$ integers:$1 + 2 + 3 + ... + (n - 1) = \frac{(n - 1)n}{2} = \frac{n(n - 1)}{2}$.For example,in a $4 	imes 4$ matrix,the number of zeros is $\frac{4(4 - 1)}{2} = \frac{12}{2} = 6$.Thus,the minimum number of zeros is $\frac{n(n - 1)}{2}$.

In an upper triangular matrix of order $n \times n$,the minimum number of zeros is:

Similar Questions

If $A = \begin{bmatrix} 1 & 0 \\ -1 & 7 \end{bmatrix}$,$I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ and $A^{2} = 8A + kI$,then the value of $k$ is

$AB = 0$,if and only if

The number of all possible matrices of order $3 \times 3$ with each entry $0$ or $1$ is:

$A$ matrix whose elements $a_{ij}$ are defined by $a_{ij} = \frac{1}{3}|i - 5j|$,where $i, j = 1, 2, 3$,is:

If $A = \frac{1}{2} \begin{bmatrix} 1 & \sqrt{3} \\ -\sqrt{3} & 1 \end{bmatrix}$,then :

Vedclass Test Series

Exam Paper Generator

Online Exam Module