Question

Let M=(aij) be a 10×10 matrix such that aij={1, if i+j=11; 0, otherwise}. Then the determination of M?​

Answer 1

$\textbf{Given:}$

$M=(a_{ij})\;\text{be a 10x10 matrix such that}$

$a_{ij}=1,\;\;\text{if i+j=11}$

$a_{ij}=0,\;\;\text{otherwise}$

$\textbf{To find:}$

$\text{Determinant of M}$

$\textbf{Solution:}$

$\text{The matrix M is}$

$\left(\begin{array}{cccccccccc}0&0&0&0&0&0&0&0&0&1\\0&0&0&0&0&0&0&0&1&0\\0&0&0&0&0&0&0&1&0&0\\0&0&0&0&0&0&1&0&0&0\\0&0&0&0&0&1&0&0&0&0\\0&0&0&0&0&1&0&0&0&0\\0&0&0&0&1&0&0&0&0&0\\0&0&0&1&0&0&0&0&0&0\\0&0&1&0&0&0&0&0&0&0\\0&1&0&0&0&0&0&0&0&0\\1&0&0&0&0&0&0&0&0&0\end{array}\right)$

$\text{Clearly, M is a diagonal matrix}$

$\textbf{We know that,}$

$\textbf{Determinant of a diagonal matrix is equal to}$

$\textbf{product of its leading diagonal elements}$

$\text{Then,}$

$\text{Determinant of M}=1{\times}1{\times}1{\times}..........\text{10 factors}$

$\implies\textbf{Determinant of M}\bf=1$

$\textbf{Answer:}$

$\textbf{Determinant of M is 1}$

Find more:

1.Prove that:det(x+y x x, 5x+4y 4x 2x, 10x+8y 8x 3x ) =x^3

https://brainly.in/question/4612859

2.The sum of the real roots of the equation | x 6 1 |

| 2 3x (x - 3)| = 0 | 3 2x (x = 2)|

is equal to (A) -4 (B) 0

(C) 6 (D) 1

https://brainly.in/question/16074720

3.If A=[102021203], prove that A3−6A2+7A+2I=0

https://brainly.in/question/8281206