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Jennifer M.

Math Educator for 17 years

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Linear Algebra

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Question:

Is the 2 x 2 matrix multiplication of 2 2 times -1 0 3 -1 8 1 equal to: -1 0 time 2 2 8 1 3 -1 In other words, does the commutative property hold for multiplication of matrices?

Jennifer M.

Answer:

Multiply it out to verify. Through multiplying the matrices it will prove that the commutative property does not hold for matrices. First 2 x 2 multiplication = 14 -2 -11 -1 Second 2 x 2 multiplication = -2 -2 19 15

Pre-Calculus

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Question:

Solve the following trigonometric equation: in the interval 0 to 360 sinx - 2 sinx cosx = 0

Jennifer M.

Answer:

Think back to algebra when we were solving equations and the various techniques we used to solve those equations. Recall factoring out the greatest common factor for example x - 2 xy what was the common factor? x was the common factor. Now let's look at sinx - 2 sinx cost = 0 Is there a greatest common factor we can factor out? sinx is the greatest common factor If we factor out sinx we will rewrite the equation to be: sinx( 1 - 2 cosx) = 0 How do we solve the equation from here? Take each factor and set it equal to 0. sinx = 0 and 1 - 2 cosx = 0 sin is equal to 0 at 0 degrees and 360 degrees therefore x = 0 and x = 360 1 - 2 cosx = 0 -1 -1 -2 cosx = -1 cosx = -1/-2 cosx = 1/2 cos is equal to 1/2 at 60 degrees and 300 degrees therefore x = 60 and 360

Geometry

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Question:

∆XYZ has coordinates at X(-2, 3) Y(-6, 0) Z(0, -8) a. First translate ∆XYZ by (x, y) —> (x – 3, y – 3) and then reflect over the line y = x. Find the new coordinates of the transformed figure. b. If you reverse the order of the composition (in other words do the reflection first and then the translation), will do the coordinates of X”, Y” and Z” change? c. Do you notice anything particular about the “movement” of the translation and the line of reflection?

Jennifer M.

Answer:

a. The new coordinates will be X" (0, -5), Y" (-3, -9), Z" (-11, -3) b. When I reverse the order, the final points are the same. c. The line of reflection and the movement and the movement of the translation have the same slope. The slope of the line of reflection is 1 and the movement of the translation is down 3 and to the left 3 or -3/-3 which equals 1. Therefore, both have the same slope which means they are parallel.

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