Write the matrix a by transforming

Assignment Help Mathematics

Reference no: EM13189166

Consider the matrix A of the linear transformation T in two dimensional space that rotates all vectors 45 degrees in the clockwise direction, and then shrinks their horizontal component by a factor of two.
a) Write the matrix A by transforming the canonical basis e1, e2 (unit vectors e1 and e2).
b) Think of T as the composition of two simpler transformations: rotation and stretching. Write the matrix for each, and check that their product equals A.
c) Describe in words the action of the transformation S which is inverse to T . Use your description of S to write its matrix B. Check that the matrix B is indeed the inverse of A.

Reference no: EM13189166

Questions Cloud

Find the width of the margins : A 25-by-33-inch sheet of paper is to be used for a poster, with the shorter side at the bottom. The margins at the sides and top are to have the same width, and the bottom margin is to be twice as wide as the other margins. Find the width of the m..

How much money is invested in bonds : Jorge purchased municipal bonds which yield 6% annually and certificates of deposit which yield 8% annually. If Jorge's initial investments amount to $11,000 and the annual income is $720, how much money is invested in bonds?

Barn owl''s right ear opens slightly upward : The barn owl's right ear opens slightly upward while its left ear opens slightly downward. This asymmetry is most useful for enabling the owl to detect the ________ of a sound.

Mitigate tribal poverty and encourage prosperity : How well do you think Native American organizations, like the Bureau of Indian Affairs, the National Congress of American Indians, and the National Indian Gaming Association, are helping Native Americans to advance?

Write the matrix a by transforming : Consider the matrix A of the linear transformation T in two dimensional space that rotates all vectors 45 degrees in the clockwise direction, and then shrinks their horizontal component by a factor of two.

Discuss the atlantic slave trade and institution of slavery : Discuss the Atlantic Slave Trade and the institution of slavery in the American south. First, discuss slavery in historical perspective, Portuguese and the Spanish filling their colonies with African slaves,

What is the correct classification of 18x : what is the correct classification of 18x?

How fast is she walking : a woman 6ft tall walks away from a light 10 ft above the ground. if her shadow lengthens at the rate of 2ft per sec, how fast is she walking?

Water vapor evaporating from pond-pressure for water : Water vapor evaporating from a pond does so as if it were diffusing across an air film 0.15 centimeters thick. The diffusion coefficient of water vapor in 20 degrees C air is about 0.25 cm^2/sec.

User Account

All Pages