AnswersPrecalculusVector Multiplication Using Matrices

Vector Multiplication Using Matrices — Quiz Answers

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1
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Which point is the coordinate of the image of cap A under the transformation the 2 by 2 matrix row 1, 0 1 row 2, 1 0 ?

A
open paren 2 comma 4 close paren
B
open paren negative 4 comma negative 2 close paren
C
open paren 4 comma 2 close paren
D
open paren negative 2 comma 4 close paren
2
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Which point is the coordinate of the image of cap A under the transformation the 2 by 2 matrix, row 1, column 1, 0 column 2, negative 1 row 2, column 1, 1 column 2, 0 ?

A
open paren negative 4 comma 2 close paren
B
open paren negative 1 comma 2 close paren
C
open paren 2 comma negative 4 close paren
D
open paren negative 1 comma 7 close paren
3

What type of transformation of triangle ABC was applied by cap t ?

A
reflect across the line y is equal to x
B
rotate 180 degrees counterclockwise about the origin
C
reflect across the line y is equal to negative x
D
rotate 270 degrees counterclockwise about the origin
4

Which transformation matrix would result in a 300 degrees counterclockwise rotation about the origin?

A
the 2 by 2 matrix, row 1, column 1, 1 half column 2, the fraction with numerator square root of 3 and denominator 2 row 2, column 1, negative the fraction with numerator square root of 3 and denominator 2 column 2, 1 half
B
the 2 by 2 matrix, row 1, column 1, negative 1 half column 2, the fraction with numerator square root of 3 and denominator 2 row 2, column 1, negative the fraction with numerator square root of 3 and denominator 2 column 2, negative 1 half
C
the 2 by 2 matrix, row 1, column 1, negative the fraction with numerator square root of 3 and denominator 2 column 2, negative 1 half row 2, column 1, 1 half column 2, negative the fraction with numerator square root of 3 and denominator 2
D
the 2 by 2 matrix, row 1, column 1, 1 half column 2, negative the fraction with numerator square root of 3 and denominator 2 row 2, column 1, the fraction with numerator square root of 3 and denominator 2 column 2, 1 half
5

Which transformation matrix would result in a 270 degrees counterclockwise rotation about the origin?

A
the 2 by 2 matrix, row 1, column 1, 0 column 2, negative 1 row 2, column 1, 1 column 2, 0
B
the 2 by 2 matrix, row 1, column 1, 0 column 2, 1 row 2, column 1, negative 1 column 2, 0
C
the 2 by 2 matrix, row 1, column 1, 1 column 2, 0 row 2, column 1, 0 column 2, negative 1
D
the 2 by 2 matrix, row 1, column 1, negative 1 column 2, 0 row 2, column 1, 0 column 2, negative 1
6

Justine reflects a vector v across the y -axis. Simonne reflects a vector v by rotating it 90 degrees counterclockwise about the origin. Which of the following vectors has the same image for Justin and Simonne?

A
the 2 by 1 column matrix row 1 negative 3 row 2 3
B
the 2 by 1 column matrix 4 3
C
the 2 by 1 column matrix 4 4
D
the 2 by 1 column matrix row 1 1 row 2 negative 1
9

Which sequence of steps would transform triangle 1 to triangle 2?

A
reflect across the x -axis; rotate 270 degrees counterclockwise about the origin
B
rotate 90 degrees counterclockwise about the origin; rotate 270 degrees counterclockwise about the origin
C
reflect across the y -axis; rotate 180 degrees counterclockwise about the origin
D
reflect across the y -axis; rotate 90 degrees counterclockwise about the origin
10

Which points are in the image of rectangle ABCD under the transformation: cap t is equal to the 2 by 2 matrix row 1, 3 0 row 2, 0 3 ?

A
cap A prime times open paren 3 comma 9 close paren ; cap b prime times open paren 12 comma 9 close paren ; cap c prime times open paren 12 comma 3 close paren ; cap d prime times open paren 3 comma 3 close paren
B
cap A prime times open paren 9 comma 3 close paren ; cap b prime times open paren 9 comma 12 close paren ; cap c prime times open paren 3 comma 12 close paren ; cap d prime times open paren 3 comma 3 close paren
C
cap A prime times open paren 4 comma 7 close paren ; cap b prime times open paren 7 comma 6 close paren ; cap c prime times open paren 7 comma 4 close paren ; cap d prime times open paren 4 comma 4 close paren
D
cap A prime times open paren 3 comma 3 close paren ; cap b prime times open paren 12 comma 3 close paren ; cap c prime times open paren 12 comma 9 close paren ; cap d prime times open paren 3 comma 12 close paren

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