Row Reduction to RREF and Rank (Linear Algebra)
Free printable university Linear Algebra worksheet on row reducing matrices to reduced row echelon form and finding the rank, including singular and rectangular matrices.
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Linear Algebra · Math worksheet
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Linear Algebra: Row Reduction to RREF and Rank
Row reduce each matrix to reduced row echelon form (every pivot is 1 with zeros above and below it) and state the rank, the number of pivots. Matrices are written in row form, e.g. [1, 2; 3, 4].
- 1.Row reduce A = [1, 1, -1; 1, 2, -5; 0, 1, -4] to reduced row echelon form and state rank(A).
- 2.Row reduce A = [1, 0, -2, 7; 0, 1, -2, 8; 0, -2, 5, -20] to reduced row echelon form and state rank(A).
- 3.Row reduce A = [1, -1, 2, 2; 0, 1, 1, 2; -1, 2, -1, 0] to reduced row echelon form and state rank(A).
- 4.Row reduce A = [1, 2, 4; -1, -1, -3] to reduced row echelon form and state rank(A).
- 5.Row reduce A = [1, 0, -2; -2, 1, 3; 0, 1, 0] to reduced row echelon form and state rank(A).
- 6.Row reduce A = [1, 0, -2, -3; 0, 0, 1, 1; -2, 0, 5, 7] to reduced row echelon form and state rank(A).
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