2.1 Systems of Linear Equations (Exercises)

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To check whether a vector is a solution of a linear system.

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To check whether a matrix is in echelon form.

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To perform row operations on a matrix.

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Checking whether a matrix is in (reduced) echelon form.

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Applying the algorithm to compute a solution of a linear system.

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Conclusions about the solutions from the structure of the echelon form.

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Solving a linear system of $2$ equations in $2$ unknowns.

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To determine the number of sulutions of a $2\times 2$ linear system.

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Identifying the size of a linear system.

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$3\times 3$ linear system 'in triangular form'.

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To solve a $3\times 3$ linear system.

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To solve a $3\times 4$ linear system.

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Two $3\times 3$-systems with the same coefficient matrix.

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To write down the augmented matrix of a linear system.

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To check whether a linear system is consistent.

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To check whether a linear system is consistent.

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To recognize row operations.

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To find the row reduced echelon form.

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To find the row reduced echelon form.

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To find the row reduced echelon form.

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To find the row reduced echelon form.

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Row reduced echelon form of a $3\times 5$-matrix.

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Solving a linear system using the augmented matrix.

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Solving a linear system using the augmented matrix.

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To solve a linear system by geometric considerations.

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How many pivots can an $m\times n$-matrix have?

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To determine which variables can be taken as free variables.

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A $2\times 2$ linear system with a parameter $h$.

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A $2\times 2$ linear system with a parameter $h$.

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Yet another $2\times 2$ linear system with a parameter $h$.

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Fourth and last $2\times 2$ linear system with a parameter $h$.

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Linear systems and pivots.

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Linear systems and pivots.

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Linear systems and pivots.

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How many 'different' echelon forms are there?

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To determine (in)consistency without computations ('by inspection').

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Freedom of free variables?

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To check whether matrices are (row) equivalent.