Evaluate each determinant in Exercises 2732. 1 1 1 2 2 2 3

Evaluate each determinant in Exercises 110. 5 7 2 3

Evaluate each determinant in Exercises 110. 4 8 5 6

Evaluate each determinant in Exercises 110. 4 1 5 6

Evaluate each determinant in Exercises 110. 7 9 2 5

Evaluate each determinant in Exercises 110. 7 14 2 4

Evaluate each determinant in Exercises 110. 1 3 8 2

Evaluate each determinant in Exercises 110. 5 1 2 7

Evaluate each determinant in Exercises 110. 15 1 6 6 5

Evaluate each determinant in Exercises 110. 12 1 2 1 8 34

Evaluate each determinant in Exercises 110. 23 1 3 12 3 4

For Exercises 1126, use Cramers rule to solve each system or to determine that the system is inconsistent or contains dependent equations. x y 7 x y 3

For Exercises 1126, use Cramers rule to solve each system or to determine that the system is inconsistent or contains dependent equations. 2x y 3 x y 3

For Exercises 1126, use Cramers rule to solve each system or to determine that the system is inconsistent or contains dependent equations. 12x 3y 15 2x 3y 13

For Exercises 1126, use Cramers rule to solve each system or to determine that the system is inconsistent or contains dependent equations. x 2y 5 5x y 2

For Exercises 1126, use Cramers rule to solve each system or to determine that the system is inconsistent or contains dependent equations. 4x 5y 17 2x 3y 3

For Exercises 1126, use Cramers rule to solve each system or to determine that the system is inconsistent or contains dependent equations. 3x 2y 2 2x 2y 3

For Exercises 1126, use Cramers rule to solve each system or to determine that the system is inconsistent or contains dependent equations. x 3y 4 3x 4y 12

For Exercises 1126, use Cramers rule to solve each system or to determine that the system is inconsistent or contains dependent equations. 2x 9y 5 3x 3y 11

For Exercises 1126, use Cramers rule to solve each system or to determine that the system is inconsistent or contains dependent equations. 3x 4y 4 2x 2y 12

For Exercises 1126, use Cramers rule to solve each system or to determine that the system is inconsistent or contains dependent equations. 3x 7y 1 2x 3y 1

For Exercises 1126, use Cramers rule to solve each system or to determine that the system is inconsistent or contains dependent equations. 2x 3y 2 5x 51 4y

For Exercises 1126, use Cramers rule to solve each system or to determine that the system is inconsistent or contains dependent equations. y 4x 2 2x 3y 8

For Exercises 1126, use Cramers rule to solve each system or to determine that the system is inconsistent or contains dependent equations. 3x 2 3y 2y 3 2x

For Exercises 1126, use Cramers rule to solve each system or to determine that the system is inconsistent or contains dependent equations. x 2y 3 0 12 8y 4x

For Exercises 1126, use Cramers rule to solve each system or to determine that the system is inconsistent or contains dependent equations. 4y 16 3x 6x 32 8y

For Exercises 1126, use Cramers rule to solve each system or to determine that the system is inconsistent or contains dependent equations. 2x 7 3y 4x 6y 3

Evaluate each determinant in Exercises 2732. 3 0 0 2 1 5 2 5 1

Evaluate each determinant in Exercises 2732. 4 0 0 3 1 4 2 3 5

Evaluate each determinant in Exercises 2732. 3 1 0 3 4 0 1 3 5

Evaluate each determinant in Exercises 2732. 2 4 2 1 0 5 3 0 4

Evaluate each determinant in Exercises 2732. 1 1 1 2 2 2 3 4 5

Evaluate each determinant in Exercises 2732. 1 2 3 2 2 3 3 2 1

In Exercises 3340, use Cramers rule to solve each system. x y z 0 2x y z 1 x 3y z 8

In Exercises 3340, use Cramers rule to solve each system. x y 2z 3 2x 3y z 9 x y 3z 11

In Exercises 3340, use Cramers rule to solve each system. 4x 5y 6z 1 x 2y 5z 12 2x y 7

In Exercises 3340, use Cramers rule to solve each system. x y z 4 x 2y z 7 x 3y 2z 4

In Exercises 3340, use Cramers rule to solve each system. x 2z 4 2y z 5 2x 3y 13

In Exercises 3340, use Cramers rule to solve each system. x 3y z 2 x 2y 8 2x y 1

In Exercises 3340, use Cramers rule to solve each system. 2x 2y 3z 10 4x y z 5 5x 2y 6z 1

In Exercises 3340, use Cramers rule to solve each system. 3x 2z 4 5x y 4 4y 3z 22

In Exercises 4142, evaluate each determinant 3 1 2 3 7 0 1 5 3 0 0 7 9 6 3 5

In Exercises 4142, evaluate each determinant 5 0 4 3 1 0 0 1 7 5 4 6 4 1 3 5

In Exercises 4344, write the system of linear equations for which Cramers rule yields the given determinants. D 2 4 3 5 , Dx 8 4 10 5

In Exercises 4344, write the system of linear equations for which Cramers rule yields the given determinants. D 2 3 5 6 , Dx 8 3 11 6

In Exercises 4548, solve each equation for x. 2 x 4 6 32

In Exercises 4548, solve each equation for x. x 3 6 x 2 4 28

In Exercises 4548, solve each equation for x. 1 x 2 3 1 1 0 2 2 8

In Exercises 4548, solve each equation for x. 2 x 1 3 1 0 2 1 4 39

Use determinants to find the area of the triangle whose vertices are (3, 5), (2, 6), and (3, 5).

Use determinants to find the area of the triangle whose vertices are (1, 1), (2, 3), and (11, 3). Determinants are used to show that three points lie on the same line (are collinear). If x1 y1 1 x2 y2 1 x3 y3 1 0, then the points (x1 , y1), (x2 , y2), and (x3 , y3) are collinear. If the determinant does not equal 0, then the points are not collinear.

Are the points (3, 1), (0, 3), and (12, 5) collinear?

Are the points (4, 6), (1, 0), and (11, 12) collinear? Determinants are used to write an equation of a line passing through two points. An equation of the line passing through the distinct points (x1 , y1) and (x2 , y2) is given by x y 1 x1 y1 1 x2 y2 1 0.

Use the determinant to write an equation for the line passing through (3, 5) and (2, 6). Then expand the determinant, expressing the lines equation in slope-intercept form.

Use the determinant to write an equation for the line passing through (1, 3) and (2, 4). Then expand the determinant, expressing the lines equation in slope-intercept form.