Question

rank of matrix (0 1 -3 1 1 0 1 1 3 1 0 2 1 1 -2 0)​

Answer 1

Answer:

rank of matrix (0 1 -3 1 1 0 1 1 3 1 0 2 1 1 -2 0)

Step-by-step explanation:

I can find but I will tell you how to find the ran of matrix

First what is rank: It's number of non-zeros row in matrix.

-> There are many ways to find rank of matrix, but I'll suggest you to go with one only the simplest one.

-> so if your matrix is of 2*2 then go for find determinant and if the determinant is equal to zero then probably your rank would be 1 and if determinant is not equal to zero then cout number of non-zero rows.

-> If your matrix is greater then 2*2 size then go for Echelon method .

->where you make your lower triangle of matrix to zero and cout the number of non-zero rows.

Answer 2

Answer:

Step-by-step explanation:

Disclaimer:

Find out the rank of matrix$\left(\begin{array}{llll}0 & 1 & -3 & 1 \\ 1 & 0 & 1 & 1 \\ 3 & 1 & 0 & 2 \\ 1 & 1 & -2 & 0\end{array}\right)$

Concept:

The concept of matrix will be used to solve the question.

Given:

The matrix which is given in the question is $\left(\begin{array}{llll}0 & 1 & -3 & 1 \\ 1 & 0 & 1 & 1 \\ 3 & 1 & 0 & 2 \\ 1 & 1 & -2 & 0\end{array}\right)$.

To Find:

We have to find out the rank of the matrix $\left(\begin{array}{llll}0 & 1 & -3 & 1 \\ 1 & 0 & 1 & 1 \\ 3 & 1 & 0 & 2 \\ 1 & 1 & -2 & 0\end{array}\right)$ .

Solution:

The nonzero determinant of highest order that can be created from a matrix's elements by arbitrarily choosing an equal number of rows and columns is known as the matrix's rank.

As many linearly independent vectors can exist in a matrix as there are non-zero rows in its row echelon matrix. Thus, all that is required to ascertain a matrix's rank is to convert it to its row echelon form and count the number of non-zero rows.

Here the matrix is $4 \times 4$ .Therefore the rank of $\left(\begin{array}{llll}0 & 1 & -3 & 1 \\ 1 & 0 & 1 & 1 \\ 3 & 1 & 0 & 2 \\ 1 & 1 & -2 & 0\end{array}\right)$ is $4$ .

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