Question

find the rank
of matrix
[ 5 3 14 4
0 1 2 1
1 -1 2 0]​

Answer 1

Answer:

find the rank

of matrix

[ 5 3 14 4

0 1 2 1

1 -1 2 0]

Step-by-step explanation:

hers ur ans

• 5
• 3
• 4
• 7
• 7

Answer 2

Concept:

We need to first  recall the concept of Rank of a matrix to solve this question.

Rank of a matrix is equal to the number of pivot elements in the matrix after applying row reduction.

i.e.  maximum number of linearly independent rows or columns of a matrix.

Given:

A matrix of the form:

$\left[\begin{array}{cccc}5&3&14&4\\0&1&2&1\\1&-1&2&0\end{array}\right]$

To find:

The rank of the matrix.

Solution:

Using row reduction method,

$R_{3}\rightarrow 5 R_{3}-R_{1}$

$\left[\begin{array}{cccc}5&3&14&4\\0&1&2&1\\0&-8&-4&-4\end{array}\right]$

$R_{3}\rightarrow R_{3}+8R_{2}$

$\left[\begin{array}{cccc}5&3&14&4\\0&1&2&1\\0&0&12&4\end{array}\right]$

So, the number of pivot elements(first leading row entry) is 3.

Hence, the rank of matrix is 3.