6 5.) (10 points) (a) Suppose TỈ : R2 → R2 s a reflection in the line y = z. what is A, the stand...

Question

Question

6 5.) (10 points) (a) Suppose TỈ : R2 → R2 s a reflection in the line y = z. what is A, the standard matrix of T1? (b) Suppos

math algebra

Answer 1

Answer #1

Muu 2. J3 24J3

Answer 2

Similar Homework Help Questions

Q3 (6 points) Let T be the rotation (counterclockwise) of R2 by an angle ofLet S...

Q3 (6 points) Let T be the rotation (counterclockwise) of R2 by an angle ofLet S R2R2 be the reflection with respect to the line y 3 x. S and T are both linear transformations. (a) (4 points) Determine the standard matrix of S. Give details about how your obtained your answer. b) (1 point) Write down the standard matrix of T. Give only the answer, no justification needed. (c) (1 point) What is the standard matrix of S。TY Drag...
1. Let T: R2 – R? be the map "reflection in the line y = x"—you...

1. Let T: R2 – R? be the map "reflection in the line y = x"—you may assume this T is linear, let Eº be the standard basis of R2 and let B be the basis given by B = a) On the graph below, draw a line (colored if possible) joining each of the points each of the points (-). (). (1) and () woits image to its image under the map T. y = x b) Find the...
linear algebra Let T: R2 R2 be a reflection in the line y = -x. Find...

linear algebra Let T: R2 R2 be a reflection in the line y = -x. Find the image of each vector. (a) (-3,9) (b) (5, -1) (c) (a,0) (d) (o, b) (e) ( ed) (f) (9)

8. 4 marks] (a) Suppose that a is the reflection across the line z y +2-0 and β is the reflection...

8. 4 marks] (a) Suppose that a is the reflection across the line z y +2-0 and β is the reflection ac oss the line y = 2. i. Show that the compositions a(β(z)) and β(a(z)) have a common fixed point in the intersection of two lines. Find this point. ii. Find complex numbers a, b, c, and d for which a(z) = a5+b and β(z) =cz+d. iii. Classify the compositions a(β(z)) and β(a(z)). (b) Let z = 21 and...
Consider the linear transformation T: R4 + R2 defined as T(11,12,13,14)=(-221 +22 +2 14,322 -14) Find...

Consider the linear transformation T: R4 + R2 defined as T(11,12,13,14)=(-221 +22 +2 14,322 -14) Find the standard matrix for T: ab sin(a) f 8 a 12 . ar What is the dimension of ker(T)? Number Is T one-to-one? Enter one yes no Write the standard matrix for HoT, where H is the reflection of R2 about the line y=1. ab sin(a) f αο α Ω TI д
Consider the following T is the reflection in the y-axis in R2: T(x, y) (-x, y),...

Consider the following T is the reflection in the y-axis in R2: T(x, y) (-x, y), v (2, -5) (a) Find the standard matrix A for the linear transformation T (b) Use A to find the image of the vector v (e) Sketch the graph of v and its image T (v) 5-4-3-21 T (v) T(v) 6 -5-4-3-2 6-5-4-3-2-1 239-lab 3 (2)pages F1 Assignment Submission For this assignment, you submit answers by question parts. The number of submissions remaining for...

ame 5. (20 points) Suppose SRR and TRR2 are linear transformations given by (o) Find the...

ame 5. (20 points) Suppose SRR and TRR2 are linear transformations given by (o) Find the standard matrix for S (asuming the standard basis for R3 and for R2) (b) Find the standard matrix for T (assuming the standard basis for IR2 and for R). (c) Show that S and T are invertible. (d) Show that T is the inverse of S (e) What is the standard matrix for T (S (x)) ToS(),where z e R27
6. (10 points) (a) (6 points) The gradient of the function o(x, y, z) at (1,2,3)...

6. (10 points) (a) (6 points) The gradient of the function o(x, y, z) at (1,2,3) is the vector (2, 1, 1) and g(1,2,3) = 1 (1) (2 points) Find the equation of the tangent plane of the level surface g(r, y, z) = 1 at (1,2,3) (ii) (2 points) Find the maximum rate of change of g(x, y, z) at (1, 2, 3). hax. rarte ot change: 23 14 (iii) (2 points) Find the rate of change of g...
question 2,7,9 please Charge 1. (10 points) What is the current through a conductor if X...

question 2,7,9 please Charge 1. (10 points) What is the current through a conductor if X electrons pass through a cross section in Y time? 2. (10 points) The current flowing through a conductor is X. If it flows for Y time, how many electrons is that X = 100 microamps, Y = 2 days 3. (10 points) A current XuA flows and Y electrons are transported. How long did it take? Resistivity 4. (10 points) An object is round...

te tt 9 Let S be the surface defined by r2 y-22= 1 and 0 15...

te tt 9 Let S be the surface defined by r2 y-22= 1 and 0 15 points by the normal direction toward the z-axis. Find the flux of the velocity field V 1and oriented (z2-ry2)i+(2.2y -yz2)j+ (y2z- 2r2)k across S Solution. To use Gauss Theorem, define C and C2 such that C1 {(a, y, z ) | a + y? < 2, z = 1} C2={(r,y,)| +y1.0} 11 TALK X W P S ww F6 & # 2 3 4...