Linear Dependence Rank Method 5

In this page linear dependence rank method 5 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 5:

Test whether the vectors (1,1,1), (1,2,3) and (2,-1,1) are linearly dependent.

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.

• 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
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• 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
  

Linear Dependence5 Rank Method to Method 1