Let T and U be the set of all orthogonal matr | vedclass

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

Question

(B) The set $A = \{-1, 0, 1\}$ is a finite set with cardinality $n(A) = 3$. The set $T$ consists of all orthogonal matrices of order $3 	imes 3$. The

Vedclass · Accepted Answer

There does not exist a bijective mapping between $A$ and $T$,or between $A$ and $U$.

Vedclass · Answer

(B) The set $A = \{-1, 0, 1\}$ is a finite set with cardinality $n(A) = 3$. The set $T$ consists of all orthogonal matrices of order $3 	imes 3$. The group of orthogonal matrices $O(3)$ is an infinite set. The set $U$ consists of all non-singular matrices of order $3 	imes 3$,which is the general linear group $GL(3, \mathbb{R})$. This is also an infinite set. $A$ bijective mapping between two sets exists if and only if they have the same cardinality. Since $n(A) = 3$ and both $T$ and $U$ are infinite sets,$n(A) 
eq n(T)$ and $n(A) 
eq n(U)$. Therefore,there does not exist a bijective mapping between $A$ and $T$,nor between $A$ and $U$.

Let $T$ and $U$ be the set of all orthogonal matrices of order $3$ over $\mathbb{R}$ and the set of all non-singular matrices of order $3$ over $\mathbb{R}$ respectively. Let $A = \{-1, 0, 1\}$. Then:

Similar Questions

Construct a $3 \times 4$ matrix,whose elements are given by $a_{i j}=\frac{1}{2}|-3 i+j|$.

If the matrices $A = \begin{bmatrix} 2 & 1 & 3 \\ 4 & 1 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & -1 \\ 0 & 2 \\ 5 & 0 \end{bmatrix}$,then $AB$ will be

If $A = \begin{bmatrix} 1 & -2 \\ 3 & 0 \end{bmatrix}$,$B = \begin{bmatrix} -1 & 4 \\ 2 & 3 \end{bmatrix}$,$C = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$,then $5A - 3B - 2C = $

If $A=\left[\begin{array}{rr}i & -i \\ -i & i\end{array}\right]$ and $B=\left[\begin{array}{rr}1 & -1 \\ -1 & 1\end{array}\right]$,then find $A^8$. (in $B$)

If $A = \begin{bmatrix} 0 & 3 \\ 0 & 0 \end{bmatrix}$ and $f(x) = x + x^2 + x^3 + \ldots + x^{2023}$,then $f(A) + I = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module