4.02 Systems of equations and row operations
Adaptive
Worksheet
Interactive practice questions
| $x$x | $y$y | $z$z | |||||
| The augmented matrix | $1$1 | $-1$−1 | $1$1 | $0$0 | is in row-echelon form and represents a linear system in $x$x, $y$y and $z$z. | ||
| $0$0 | $1$1 | $-1$−1 | $4$4 | ||||
| $0$0 | $0$0 | $1$1 | $-6$−6 |
| Solve for $x$x, $y$y and $z$z. |
Medium
4min
| The augmented matrix | $1$1 | $-4$−4 | $2$2 | $7$7 | is in row-echelon form and represents a linear system in $x$x, $y$y and $z$z. | ||
| $0$0 | $1$1 | $-7$−7 | $6$6 | ||||
| $0$0 | $0$0 | $0$0 | $0$0 |
| Solve for $x$x, $y$y and $z$z. If the system has an infinite number of solutions, express $x$x and $y$y in terms of $z$z. |
Medium
3min
| The augmented matrix | $1$1 | $0$0 | $2$2 | $5$5 | is in row-echelon form and represents a linear system in $x$x, $y$y and $z$z. | ||
| $0$0 | $1$1 | $-7$−7 | $3$3 | ||||
| $0$0 | $0$0 | $0$0 | $0$0 |
| Solve for $x$x, $y$y and $z$z. If the system has an infinite number of solutions, express $x$x and $y$y in terms of $z$z. |
Medium
1min
Consider the system of equations:
| $-x+y$−x+y | $=$= | $-3$−3 |
| $2x+3y$2x+3y | $=$= | $16$16 |
Medium
1min
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