trig ch4

Question 1

lines with no solutions

Answer 1

parallel

Question 2

consistent independent lines

Answer 2

intersecting, 1 solution

Question 3

consistent dependent lines

Answer 3

infinitely many solutions (same line)

Question 4

cases |x+?|

Answer 4

find zeros, x> or x< zeros

Question 5

determinant of
[a b]
[c d]

Answer 5

ad-cb

Question 6

determinant of
[a b c]
[d e f]
[g h i]

Answer 6

aei +bfg+cdh -gec -hfa - idb (rule of sarrus)

Question 7

dot product multiply2
[a b]*[c]
[d]

Answer 7

• [ac+ bd]

- not commutative

Question 8

matrix dimensions [row1 column 1] * [row2 column2]2

Answer 8

• it is able to be multiplied if column1=row2

- product dimensions are row1 x column2

Question 9

determinant solutions meaning4

Answer 9

• det=/ 0 –> 1 solution
• det=0 –> infinite or zero solutions
• area original shape times determinant =area of new shape
• negative determinant means order of points was reversed

Question 10

solve using inverse matrices

Answer 10

left multiply by []^-1

Question 11

linear programing theorem

Answer 11

max and min values of the objective occur at the vertices of the feasibility region

Question 12

distance between two ordered triples (x,y,z) (a,b,c)

Answer 12

sqroot((x-a)^2+(y-b)^2+(z-c)^2)

Question 13

dilation by factor k with respect to y axis

Answer 13

1 0

0 k

Question 14

dilation by factor k with respect to x axis

Answer 14

k 0

0 1

Question 15

dilation by factor k with respect to origin

Answer 15

k 0

0 k

Question 16

shear by factor k with respect to x axis

Answer 16

1 k

0 1

Question 17

reflection over y=x

Answer 17

0 1

1 0

Question 18

rotation by -90 with respect to origin

Answer 18

0 1

-1 0

Question 19

rotation by 90 with respect to origin

Answer 19

0 -1

1 0