Homework Answers
Add Answer to:
3. (6 points/2 each) Let T:R2 + R2. State why T is not linear. (a) T(C1,...
Let T:R2 → R2 be the linear transformation that first reflects points
Let T:R2 → R2 be the linear transformation that first reflects points through the x-axis and then then reflects points through the line y = -x. Find the standard matrix A for T.
Q8 6 Points Let T : R2 + Rº be a linear transformation with PT(x) =...
Q8 6 Points Let T : R2 + Rº be a linear transformation with PT(x) = x2 – 1. Decide whether or not such a T is always diagonalizable. Justify your answer.. Q8.2 3 Points Determine/Compute the linear transformation T2 : R2 + R2, VH T(T(u)).
Problem 4 Let T:R2 R2 be defined by and a be the standard basis for R2....
Problem 4 Let T:R2 R2 be defined by and a be the standard basis for R2. a) Find the matrix of T with respect to a, (T): b) Let 3 be the basis { 1 -1}. Find (T18 c) Find (7)
Problem 6. (6 points) (a) Explain why В-Q.(.)}form a basis for R2 forms a basis for...
Problem 6. (6 points) (a) Explain why В-Q.(.)}form a basis for R2 forms a basis for R2 (b) Find the coordinate vector of in the basis (c) Suppose the standard matrix of a linear transformation T:R2 R2 is 2-3 Find the matrix of T with respect to the basis B, i.e., find [T]B.
2. (5 points) Let T: R2 + R3 be a linear transformation with 2x1 - x2]...
2. (5 points) Let T: R2 + R3 be a linear transformation with 2x1 - x2] 1-3x1 + x2 | 2x1 – 3x2 Find x = (x) <R? such that [0] -1 T(x) = (-4)
show steps! Let T:R2-R2 be multiplication by A. Determine whether T has an inverse; if so,...
show steps!
Let T:R2-R2 be multiplication by A. Determine whether T has an inverse; if so, find X2 5 81 -3 3 A- If inverse exists enter y1 and y2, otherwise enter NA for both. Click here to enter or edit your answer
X1 Let x = V = and v2 - and let T: R2R2 be a linear...
X1 Let x = V = and v2 - and let T: R2R2 be a linear transformation that maps x into xxv, + XxV2. Find a matrix A such that T(x) is Ax for each x. X2 A= Assume that is a linear transformation. Find the standard matrix of T. T:R3-R2, T(41) = (1,3), and T(62) =(-4,6), and T(03) = (3. – 2), where e1, 22, and ez are the columns of the 3*3 identity matrix. A= (Type an integer...
Find the most general real-valued solution to the linear system of differential equations x⃗ ′=[1−34−6]x⃗ .x→′=[14−3−6]x→....
Find the most general real-valued solution to the linear system
of differential equations x⃗ ′=[1−34−6]x⃗
.x→′=[14−3−6]x→.
⎡⎣⎢⎢[
x1(t)x1(t)
⎤⎦⎥⎥]
x2(t)x2(t)
=c1=c1
⎡⎣⎢⎢[
⎤⎦⎥⎥]
+ c2+ c2
⎡⎣⎢⎢[
⎤⎦⎥⎥]
a. Find the most general real-valued solution to the linear system of differential equations a = [_3_-4). 1 4 3 - 6 xit) = C1 + C2 22(t) b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle center point /...
4. (22 points) Let To : R2 R2 be the linear transformation that rotates each point in IR2 about the origin through an angle of θ (with counterclockwise corresponding to a positive angle), and let T,p...
4. (22 points) Let To : R2 R2 be the linear transformation that rotates each point in IR2 about the origin through an angle of θ (with counterclockwise corresponding to a positive angle), and let T,p : R2 → R2 be defined similarly for the angle φ. (a) (8 points) Find the standard matrices for the linear transformations To and To. That is, let A be the matrix associated with Tip, and let B be the matrix associated with To....
Let T be the linear transformation from R3 into R2 defined by (1) For the standard...
Let T be the linear transformation from R3 into R2 defined by (1) For the standard ordered bases a and ß for R3 and IR2 respectively, find the associated matrix for T with respect to the bases α and β. (2) Let α = {x1 , X2, X3) and β = {yı, ys), where x1 = (1,0,-1), x2 = - (1,0). Find the associated (1,1,1), хз-(1,0,0), and y,-(0, 1), Уг matrices T]g and T12
Q8 6 Points Let T : R2 + Rº be a linear transformation with PT(x) = x2 – 1. Decide whether or not such a T is always diagonalizable. Justify your answer.. Q8.2 3 Points Determine/Compute the linear transformation T2 : R2 + R2, VH T(T(u)).
Problem 4 Let T:R2 R2 be defined by and a be the standard basis for R2. a) Find the matrix of T with respect to a, (T): b) Let 3 be the basis { 1 -1}. Find (T18 c) Find (7)
Problem 6. (6 points) (a) Explain why В-Q.(.)}form a basis for R2 forms a basis for R2 (b) Find the coordinate vector of in the basis (c) Suppose the standard matrix of a linear transformation T:R2 R2 is 2-3 Find the matrix of T with respect to the basis B, i.e., find [T]B.
2. (5 points) Let T: R2 + R3 be a linear transformation with 2x1 - x2] 1-3x1 + x2 | 2x1 – 3x2 Find x = (x) <R? such that [0] -1 T(x) = (-4)
show steps!
Let T:R2-R2 be multiplication by A. Determine whether T has an inverse; if so, find X2 5 81 -3 3 A- If inverse exists enter y1 and y2, otherwise enter NA for both. Click here to enter or edit your answer
X1 Let x = V = and v2 - and let T: R2R2 be a linear transformation that maps x into xxv, + XxV2. Find a matrix A such that T(x) is Ax for each x. X2 A= Assume that is a linear transformation. Find the standard matrix of T. T:R3-R2, T(41) = (1,3), and T(62) =(-4,6), and T(03) = (3. – 2), where e1, 22, and ez are the columns of the 3*3 identity matrix. A= (Type an integer...
Find the most general real-valued solution to the linear system
of differential equations x⃗ ′=[1−34−6]x⃗
.x→′=[14−3−6]x→.
⎡⎣⎢⎢[
x1(t)x1(t)
⎤⎦⎥⎥]
x2(t)x2(t)
=c1=c1
⎡⎣⎢⎢[
⎤⎦⎥⎥]
+ c2+ c2
⎡⎣⎢⎢[
⎤⎦⎥⎥]
a. Find the most general real-valued solution to the linear system of differential equations a = [_3_-4). 1 4 3 - 6 xit) = C1 + C2 22(t) b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle center point /...
4. (22 points) Let To : R2 R2 be the linear transformation that rotates each point in IR2 about the origin through an angle of θ (with counterclockwise corresponding to a positive angle), and let T,p : R2 → R2 be defined similarly for the angle φ. (a) (8 points) Find the standard matrices for the linear transformations To and To. That is, let A be the matrix associated with Tip, and let B be the matrix associated with To....
Let T be the linear transformation from R3 into R2 defined by (1) For the standard ordered bases a and ß for R3 and IR2 respectively, find the associated matrix for T with respect to the bases α and β. (2) Let α = {x1 , X2, X3) and β = {yı, ys), where x1 = (1,0,-1), x2 = - (1,0). Find the associated (1,1,1), хз-(1,0,0), and y,-(0, 1), Уг matrices T]g and T12
Most questions answered within 3 hours.
-
What are the main components of the fermentation process and
give an explanation of each? Include...
asked 18 minutes ago -
Explain which types of cells in the body (belonging to which
organs, etc.) are sensitive to...
asked 22 minutes ago -
A single cable supports an 703-kg elevator car. What is the
tension in the cable when...
asked 24 minutes ago -
among the three different ways to link CSS specifications to an
HTML document (inline CSS, document...
asked 36 minutes ago -
(1) Write the net ionic equation for the reaction that occurs
when equal volumes of 0.191...
asked 1 hour ago -
On the night of April 18, 1775, a signal was to be sent from the
Old...
asked 46 minutes ago -
For each of the following strong base solutions, determine
[OH−],[H3O+], pH, and pOH 4.8 x 10^-4...
asked 41 minutes ago -
The magnitude of the electric field inside a capacitor is 6.6 x
106 N/C. What is...
asked 41 minutes ago -
Organizations may have only a few products or many products in a
product line. Consider Campbell...
asked 55 minutes ago -
could you please help me to explain the nmr splitting
integration and chemical shift and assignment...
asked 51 minutes ago -
A
29.0 cm diameter coil consists of 23 turns of cylindrical copper
wire 2.00 mm in...
asked 57 minutes ago -
Q1
Two of your friends each received the results of their
first midterm exam this term....
asked 1 hour ago