Let T 1 </msub> be a reflection of <mi mathvariant="double-struck">R 3

Petrovcic2x 2022-06-24 Answered
Let T 1 be a reflection of R 3 in the xy plane, T 2 is a reflection of R 3 in the xz plane. What is the standard matrix of transformation T 2 T 1 ?
Here's my thinking so far:
Since the standard matrix for reflections in xy is
[ 1 0 0 0 1 0 0 0 0 ]
Similarly, standard matrix for orthogonal projection in the xz plane is
[ 1 0 0 0 0 0 0 0 1 ]
I could multiply
[ 1 0 0 0 0 0 0 0 1 ] [ 1 0 0 0 1 0 0 0 0 ]
to yield
[ 1 0 0 0 0 0 0 0 0 ]
Could someone confirm for me if this is a valid approach?
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)

Braylon Perez
Answered 2022-06-25 Author has 34 answers
Reflection in the xy plane has matrix
[ 1 0 0 0 1 0 0 0 1 ]
and similar for reflection in the xz plane.
Your matrices, as you say once, are for projection, rather than reflection. If you reflect in the xy plane, the x and y values stay the same, but the z-value becomes its negative.
Your idea of multplying the matrices is correct.

We have step-by-step solutions for your answer!

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 2021-06-13
For the matrix A below, find a nonzero vector in Nul A and a nonzero vector in Col A.
A=[2359891121431727]
Find a nonzero vector in Nul A.
A=[3201]
asked 2021-09-13

Assume that A is row equivalent to B. Find bases for Nul A and Col A.
A=[12511324515212045365192]
B=[12045005780000900000]

asked 2021-09-18

Find an explicit description of Nul A by listing vectors that span the null space.
A=[154310121000000]

asked 2021-11-16
Write the system first as a vector equation and then as a matrix equation.
8x1x2=4
5x1+4x2=1
x13x2=2
asked 2022-07-24

a5=0 and a15=4 what is the sum of the first 15 terms of that arithmetic sequence

asked 2022-06-14
I have a matrices A K × M and B K × N I am looking for an orthogonal matrix T M × N such that minimize:
a r g m i n T | | A T B | |
(on other words: the best orthogonal transformation from A to B).
how can I find this T?
asked 2022-06-24
Linear transformation and its matrix
two bases:
A = { v 1 , v 2 , v 3 } and B = { 2 v 1 , v 2 + v 3 , v 1 + 2 v 2 v 3 }
There is also a linear transformation: T : R 3 R 3
Matrix in base A:
M T A = [ 1 2 3 4 5 6 1 1 0 ]
Now I am to find matrix of the linear transformation T in base B.
I have found two transition matrixes (from base A to B and from B to A):
P A B = [ 2 0 1 0 1 2 0 1 1 ]
( P A B ) 1 = P B A = [ 1 2 1 6 1 6 0 1 3 2 3 0 1 3 1 3 ]
How can I find M T B ?

New questions