The number of symmetric matrices of order 3 t | vedclass

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

Question

(D) symmetric matrix $A$ of order $3 	imes 3$ is defined as $A = A^T$. For a $3 	imes 3$ matrix,it takes the form: $A = \begin{bmatrix} a & b & c \

Vedclass · Accepted Answer

$10^6$

Vedclass · Answer

(D) symmetric matrix $A$ of order $3 	imes 3$ is defined as $A = A^T$. For a $3 	imes 3$ matrix,it takes the form: $A = \begin{bmatrix} a & b & c \ b & d & e \ c & e & f \end{bmatrix}$ Here,the independent entries are $a, b, c, d, e,$ and $f$. There are $6$ independent positions in the matrix that can be filled. Each of these $6$ positions can be filled by any of the $10$ digits from the set $\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$. Therefore,the total number of such symmetric matrices is $10 	imes 10 	imes 10 	imes 10 	imes 10 	imes 10 = 10^6$.

The number of symmetric matrices of order $3 \times 3$,with all the entries from the set $\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$,is:

Similar Questions

Solve the equation for $x, y, z$ and $t$ if
$2\begin{bmatrix} x & z \\ y & t \end{bmatrix} + 3\begin{bmatrix} 1 & -1 \\ 0 & 2 \end{bmatrix} = 3\begin{bmatrix} 3 & 5 \\ 4 & 6 \end{bmatrix}$

If $A = \begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix}$,then $A^{10} = $ . . . . . . .

The matrix $\begin{bmatrix} 2 & 5 & -7 \\ 0 & 3 & 11 \\ 0 & 0 & 9 \end{bmatrix}$ is known as:

Assuming that the sums and products given below are defined,which of the following is not true for matrices?

If $A$ and $B$ are square matrices of the same order such that $AB = BA$,then prove by induction that $AB^{n} = B^{n}A$. Further,prove that $(AB)^{n} = A^{n}B^{n}$ for all $n \in N$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module