The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
x
+14 votes
1.5k views

The rank of the matrix given below is:

$$\begin{bmatrix} 1 &4 &8 &7\\ 0 &0& 3 &0\\ 4 &2& 3 &1\\ 3 &12 &24 &2 \end{bmatrix}$$

  1. $3$
  2. $1$
  3. $2$
  4. $4$
asked in Linear Algebra by Veteran (59.9k points)
edited by | 1.5k views

3 Answers

+19 votes
Best answer

It's an non-singular 4x4 matrix, hence its rank is 4. A non-singular matrix has non-zero determinant.


(D) is correct option!

answered by Loyal (6.1k points)
edited by
+4

see this..

+1
If you have a look at your solution again, you will find that you've jotted down the question wrong.The element at (2,4) is 21( not 2) which would make the first and second rows linearly dependent. Hence rank can't be 4.

It is 3.
0
If we take 2 then it would be rank =4 and if we consider 21 then rank would  be 3
0 votes
Answer D. 4
To calculate matrix rank transform matrix to upper triangular form using elementary row operations.
  A1 A2 A3 A4
1 1 4 8 7
2 0 0 3 0
3 4 2 3 1
4 3 12 24 2

Multiply the 1st row by 4.  R1->R1×4

  A1 A2 A3 A4
1 4 16 32 28
2 0 0 3 0
3 4 2 3 1
4 3 12 24 2

Subtract the 1st row from the 3rd row and restore it       R3->R3-R1

  A1 A2 A3 A4
1 1 4 8 7
2 0 0 3 0
3 0 -14 -29 -27
4 3 12 24 2

Multiply the 1st row by 3.  R1-->R1×3

  A1 A2 A3 A4
1 3 12 24 21
2 0 0 3 0
3 0 -14 -29 -27
4 3 12 24 2

Subtract the 1st row from the 4th row and restore it.    R4-->R4-R1

  A1 A2 A3 A4
1 1 4 8 7
2 0 0 3 0
3 0 -14 -29 -27
4 0 0 0 -19

Swap the 2nd and the 3rd rows R2<->R3

  A1 A2 A3 A4
1 1 4 8 7
2 0 -14 -29 -27
3 0 0 3 0
4 0 0 0 -19

Calculate the number of linearly independent rows

  A1 A2 A3 A4
1 1 4 8 7
2 0 -14 -29 -27
3 0 0 3 0
4 0 0 0

-19

 
answered ago by Active (2.2k points)
–1 vote
Correct Question -->

The rank of the matrix given below is:

    1    4    8     7
    0    0    3     0
    4    2    3     1
    3   12  24    21

 

 

 

Since R4=3R1 Then Rank != 4

now try for rank of 3

                1  4  8          
                0  0  3   = -3 *   1   4    = -3 * -14 =52
                4  2  3               4   2
  
      here 52 != 0
    So, Rank of the given matrix is = 3
answered by (309 points)
Answer:

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
47,913 questions
52,296 answers
182,255 comments
67,748 users