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blackblanx
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Homework Statement
For Any 5 x 3 matrix A, explain why rows of A must be linearly dependent.
The Attempt at a Solution
No idea please drop a hint
What dimension are the rows? How many of them are there?blackblanx said:Homework Statement
For Any 5 x 3 matrix A, explain why rows of A must be linearly dependent.
The Attempt at a Solution
No idea please drop a hint
Linear dependence in a 5 x 3 matrix refers to the relationship between the rows or columns of the matrix. It means that one or more rows or columns can be expressed as a linear combination of the other rows or columns in the matrix.
To determine if a 5 x 3 matrix is linearly dependent, you can perform row operations on the matrix and look for any rows or columns that can be expressed as a linear combination of the other rows or columns. If there are any, then the matrix is linearly dependent.
Linear dependence in a 5 x 3 matrix can indicate that there is redundancy or overlap in the data represented by the matrix. This can affect the accuracy of any calculations or analysis done using the matrix.
Yes, a 5 x 3 matrix can be linearly dependent in both the rows and columns. This means that there are relationships between both the rows and columns that can be expressed as linear combinations of each other.
To fix linear dependence in a 5 x 3 matrix, you can perform row operations to transform the matrix into a new matrix that is linearly independent. This can involve rearranging rows or columns, or performing operations such as row reduction or row replacement.