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How do you find rank of a matrix?

First, You have to reduce the matrix to echelon form . The number of nonzero rows in the reduced echelon form matrix (number of linearly independent rows) indicates the rank of the matrix. Go to any search engine and type "Rank of a matrix, Cliffnotes" for an example.


How can you identify a dependent or inconsistent system by looking at an augmented matrix in reduced row echelon form?

I bet it can be done, but I'll be darned if I can!


Which of the following 33 matrices are in reduced row-echelon form?

1 1 1 1 2 2 2 2 3 3 3 3


What is reduced row echelon form mean?

Reduced row echelon form (RREF) is a specific form of a matrix used in linear algebra. A matrix is in RREF if it satisfies three conditions: each leading entry (the first non-zero number from the left in a non-zero row) is 1, each leading 1 is the only non-zero entry in its column, and the leading 1s move to the right as you move down the rows. RREF is useful for solving systems of linear equations and determining the rank of a matrix.


Is every square matrix is a product of elementary matrices explain?

Yes, every square matrix can be expressed as a product of elementary matrices. This is because elementary matrices, which perform row operations, can be used to transform any square matrix into its row echelon form or reduced row echelon form through a series of row operations. Since any square matrix can be transformed into the identity matrix using these operations, it can be represented as a product of the corresponding elementary matrices that perform these transformations. Thus, every square matrix is indeed a product of elementary matrices.