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2.02 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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Outcomes

A2.N.M.A.3

Create and use augmented matrices to solve systems of linear equations in real-world contexts, by hand and using technology.*

A2.MP1

Make sense of problems and persevere in solving them.

A2.MP2

Reason abstractly and quantitatively.

A2.MP3

Construct viable arguments and critique the reasoning of others.

A2.MP4

Model with mathematics.

A2.MP5

Use appropriate tools strategically.

A2.MP6

Attend to precision.

A2.MP7

Look for and make use of structure.

A2.MP8

Look for and express regularity in repeated reasoning.

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