Linear Dependence Rank Method 2

In this page linear dependence rank method 2 we are going to see some example problem to understand how to test whether the given vectors are linear dependent.

Procedure for  Method II

• First we have to write the given vectors as row vectors in the form of matrix.
• Next we have to use elementary row operations on this matrix in which all the element in the nth column below the nth element are zero.
• The row which is having every element zero should be below the non zero row.
• Now we have to count the number of non zero vectors in the reduced form. If number of non zero vectors = number of given vectors,then we can decide that the vectors are linearly independent. Otherwise we can say it is linearly dependent.

Example 2:

Test whether the vectors (1,3,1), (-1,1,1) and (3,1,-1) are linearly dependent.If so write the relationship for the vectors

Solution:

Number of non zero rows is 2. So rank of the given matrix = 2.

If number of non zero vectors = number of given vectors,then we can decide that the vectors are linearly independent. Otherwise we can say it is linearly dependent.

Here rank of the given matrix is 2 which is less than the number of given vectors.So that we can decide the given vectors are linearly dependent. linear dependence2 rank method

Related pages

• Types of matrices
• Equality of matrices
• Operation on matrices
• Algebraic properties of matrices
• Multiplication properties
• Minor of a matrix
• Practice questions of minor of matrix
• Adjoint of matrix
• Adjoint of matrix worksheets
  
• Determinant of matrix
• Inverse of a matrix
• Practice questions of inverse of matrix
• Inversion method
• Inversion method worksheets
• Cramer's Rule for 3 equations
• Cramer's Rule for 2 equations
• Solving 2 equations using Cramer's method
• Rank Method in Matrix
• Rank of a matrix
• Solving using rank method
• Linear dependence of vectors
• Linear dependence of vectors in rank method
• Characteristic Equation of matrix
• Characteristic vector of matrix
• Diagonalization of matrix
• Gauss elimination method
  
• Matrix calculator
• Matrix worksheets