Let M=(aij) be a 10×10 matrix such that aij={1, if i+j=11; 0, otherwi

1.	Let M=(aij) be a 10×10 matrix such that aij={1, if i+j=11; 0, otherwise}. Then the determination of M?
Answer» $\textbf{Given:}$ $M=(a_{ij})\;\text{be a 10x10 matrix such that}$ $a_{ij}=1,\;\;\text{if i+j=11}$ $a_{ij}=0,\;\;\text{otherwise}$ $\textbf{To find:}$ $\text{Determinant of M}$ $\textbf{Solution:}$ $\text{The matrix M is}$ $\left(\begin{array}{cccccccccc}0&0&0&0&0&0&0&0&0&1\\0&0&0&0&0&0&0&0&1&0\\0&0&0&0&0&0&0&1&0&0\\0&0&0&0&0&0&1&0&0&0\\0&0&0&0&0&1&0&0&0&0\\0&0&0&0&0&1&0&0&0&0\\0&0&0&0&1&0&0&0&0&0\\0&0&0&1&0&0&0&0&0&0\\0&0&1&0&0&0&0&0&0&0\\0&1&0&0&0&0&0&0&0&0\\1&0&0&0&0&0&0&0&0&0\end{array}\right)$ $\text{Clearly, M is a diagonal matrix}$ $\textbf{We know that,}$ $\textbf{Determinant of a diagonal matrix is <klux>EQUAL</klux> to}$ $\textbf{product of its leading diagonal elements}$ $\text{Then,}$ $\text{Determinant of M}=1{\times}1{\times}1{\times}..........\text{10 factors}$ $\implies\textbf{Determinant of M}\bf=1$ $\textbf{Answer:}$ $\textbf{Determinant of M is 1}$ Find more: 1.Prove that:det(x+y x x, 5x+4y 4X 2x, 10x+8y 8x 3x ) =x^3 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 brainly.in/question/16074720 3.If A=[102021203], prove that A3−6A2+7A+2I=0 brainly.in/question/8281206

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

Answer»

$\textbf{Given:}$

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

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

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

$\textbf{To find:}$

$\text{Determinant of M}$

$\textbf{Solution:}$

$\text{The matrix M is}$

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