Give the standard matrix of the linear transformation that first sends (x, y, z) to (y, y, z), and rotates this vector 90 degrees counterclockwise about the origin in the x = y plane. Find standard matrix of linear transformation.

Julia Chang 2022-09-25 Answered
Give the standard matrix of the linear transformation that first sends (x, y, z) to (y, y, z), and rotates this vector 90 degrees counterclockwise about the origin in the x = y plane. Find standard matrix of linear transformation.
You can still ask an expert for help

Want to know more about Matrix transformations?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

niveaus7s
Answered 2022-09-26 Author has 8 answers
MathJax(?): Can't find handler for document MathJax(?): Can't find handler for document Use a composition: math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> T: R 2 R 2 . T ( x , y , z ) ( y , y , z ). What is the matrix for a rotation of 90 degrees? Not hard to find. Call it R: R 2 R 2 defined by a matrix. (considers sin and cos as a 2 × 2 matrix). Using these facts, do you think you could come up with a composition involving the transformations math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> T and math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> R to find the desired linear transformation?
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-09-13

Suppose that A is row equivalent to B. Find bases for the null space of A and the column space of A.
A=[12511324515212045365192]
B=[12045005780000900000]

asked 2021-09-18

I need to find a unique description of Nul A, namely by listing the vectors that measure the null space.
A=[154310121000000]

asked 2021-06-13

For the matrix A below, find a nonzero vector in the null space of A and a nonzero vector in the column space of A
A=[2359891121431727] 
Find a vector in the null space of A that is not the zero vector 
A=[3201]

asked 2021-01-25

Let D be the diagonal subset D={(x,x)xS3} of the direct product S3×S3. Prove that D is a subgroup of S3×S3 but not a normal subgroup.

asked 2022-09-09
How to find a matrix of linear transformation f : R n M a t ( n , n ) .
Let's say we do f : R 2 M a t ( 2 , 2 ) given by f ( x , y ) = [ x 2 y x + y x ]
We calculate image of canonical basis f ( 1 , 0 ) = [ 1 0 1 1 ] and f ( 0 , 1 ) = [ 0 2 1 0 ]
Now the problematic part, ever since when caltulating matrix from vectors R n R m the approach is to transpose images of standard base ( f ( 1 , 0 , . . . , 0 ) T | f ( 0 , 1 , . . . , 0 ) T | f ( 0 , 0 , . . . , 1 ) T ). We can solve the R M a t problem by using ( A T | B T | C T . . . ), of course, but is there any way how to shrink the vector so we can succeed something like ( A T | B T | C T . . . )?
asked 2021-12-13
Find the characteristic equation and the eigenvalues (and corresponding eigenvectors) of the matrix.
[223032012]
a) The characteristic equation
λ37λ2+14λ8=0
b) The eigenvalues
(λ1, λ2, λ3)=(1, 2, 4)
The corresponding eigenvectors
x1=7, 1, 1?
x2=1, 0, 0
x3=13, 4, 2?
asked 2021-02-12

Write the given matrix equation as a system of linear equations without matrices.
[201030110][xyz]=[695]

New questions