Let T1 be the reflection about the line 4x-5y=0 and T2 be the reflection about the line -4x-1y=0 in the euclidean plane.
(i) The standard matrix of T1*T2 is:
[_,_]
[_,_]
Thus T1T2 is a counterclockwise rotation about the origin by an angle of _____ radians.
(ii) The standard matrix of T2*T1 is:
[_,_]
[_,_]
Thus T2T1 is a counterclockwise rotation about the origin by an angle of _____ radians.
Solution
this is for similar problem Let T1 be the reflection about the line 2x–5y=0 and T2 be the reflection about the line –4x+3y=0 in the euclidean plane. (i) The standard matrix of T1 o T2 is: ? I think these equations are correct... T(v) = A(v) Reflection: A = [((2(u_1))^2)), (2(u_1)(u_2))) (2(u_1)(u_2)), ((2(u_2))^2))] *u being the unit vectors Rotation counterclockwise: A = [cosx -sinx sinx cosx] S o T is the matrix Transformation with matrix AB 3. The attempt at a solution I thought I understood this, but again, I guess I\'ve understood something incorrectly. For the first question, I got the unit vectors to be: [(5/sqrt29)], (2/sqrt29)] and [(3/5), (4/5)] for T_1 and T_2 respectively. I then got the standard matrix A of T_1 to be: [(21/29) (20/29) (20/29) (-21/29)] and the standard matrix B of T_2 to be: [(-7/25) (24/25) (24/25) (7/25)] I then took AB = the dot product of these matrices to get: [(333/6350) (644/6350) (-644/6350) (333/6350)]
.
Web & Social Media Analytics Previous Year Question Paper.pdf
Let T1 be the reflection about the line 4x-5y-0 and T2 be the reflecti.docx
1. Let T1 be the reflection about the line 4x-5y=0 and T2 be the reflection about the line -4x-1y=0
in the euclidean plane.
(i) The standard matrix of T1*T2 is:
[_,_]
[_,_]
Thus T1T2 is a counterclockwise rotation about the origin by an angle of _____ radians.
(ii) The standard matrix of T2*T1 is:
[_,_]
[_,_]
Thus T2T1 is a counterclockwise rotation about the origin by an angle of _____ radians.
Solution
this is for similar problem Let T1 be the reflection about the line 2x–5y=0 and T2 be the
reflection about the line –4x+3y=0 in the euclidean plane. (i) The standard matrix of T1 o T2
is: ? I think these equations are correct... T(v) = A(v) Reflection: A = [((2(u_1))^2)),
(2(u_1)(u_2))) (2(u_1)(u_2)), ((2(u_2))^2))] *u being the unit vectors Rotation
counterclockwise: A = [cosx -sinx sinx cosx] S o T is the matrix Transformation with matrix AB
3. The attempt at a solution I thought I understood this, but again, I guess I've understood
something incorrectly. For the first question, I got the unit vectors to be: [(5/sqrt29)], (2/sqrt29)]
and [(3/5), (4/5)] for T_1 and T_2 respectively. I then got the standard matrix A of T_1 to be:
[(21/29) (20/29) (20/29) (-21/29)] and the standard matrix B of T_2 to be: [(-7/25) (24/25)
(24/25) (7/25)] I then took AB = the dot product of these matrices to get: [(333/6350) (644/6350)
(-644/6350) (333/6350)]
![Let T1 be the reflection about the line 4x-5y=0 and T2 be the reflection about the line -4x-1y=0
in the euclidean plane.
(i) The standard matrix of T1*T2 is:
[_,_]
[_,_]
Thus T1T2 is a counterclockwise rotation about the origin by an angle of _____ radians.
(ii) The standard matrix of T2*T1 is:
[_,_]
[_,_]
Thus T2T1 is a counterclockwise rotation about the origin by an angle of _____ radians.
Solution
this is for similar problem Let T1 be the reflection about the line 2x–5y=0 and T2 be the
reflection about the line –4x+3y=0 in the euclidean plane. (i) The standard matrix of T1 o T2
is: ? I think these equations are correct... T(v) = A(v) Reflection: A = [((2(u_1))^2)),
(2(u_1)(u_2))) (2(u_1)(u_2)), ((2(u_2))^2))] *u being the unit vectors Rotation
counterclockwise: A = [cosx -sinx sinx cosx] S o T is the matrix Transformation with matrix AB
3. The attempt at a solution I thought I understood this, but again, I guess I've understood
something incorrectly. For the first question, I got the unit vectors to be: [(5/sqrt29)], (2/sqrt29)]
and [(3/5), (4/5)] for T_1 and T_2 respectively. I then got the standard matrix A of T_1 to be:
[(21/29) (20/29) (20/29) (-21/29)] and the standard matrix B of T_2 to be: [(-7/25) (24/25)
(24/25) (7/25)] I then took AB = the dot product of these matrices to get: [(333/6350) (644/6350)
(-644/6350) (333/6350)]](https://image.slidesharecdn.com/lett1bethereflectionabouttheline4x-5y-0andt2bethereflecti-230204030504-b2f62343/85/Let-T1-be-the-reflection-about-the-line-4x-5y-0-and-T2-be-the-reflecti-docx-1-320.jpg)
