5. Consider a linear transformation T R-R2 which reflects a vector about the line y=-r, and dilates the refected vector by a factor of 2. Find the standard matrix for the linear transformation
5. Consider a linear transformation T R-R2 which reflects a vector about the line y=-r, and dilates the refected vector by a factor of 2. Find the standard matrix for the linear transformation
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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can you solve number 5
![3. Consider a matrix A=
8.
Find the characteristic equation of the matrix A, and then find the eigenvalues and
cigenvectors.
4. Find the standard matrix for T where Tryr,)3(2x,+ -2r,).
5. Consider a linear transfomation T R- R which refects a vector about the line
y--r. and dilates the reflected vector by a factor of 2. Find the standard matrix for
the linear transformation.
[102]
6 Find the kemnel of the linear transformation whose standard matnx is B-215
[237]
7. Consider the transformation tw 5r,-3r, w, =2r, +a, Detemmine whether the
transformation is one-to-one.
8 Find the canonical basis for the solution space of the homogeneous system.
+2,+ + =0
2+5,+3r,+2x,0
2+3+2,+ ,=0
9. Find a basis for the hyperplane a where aF2,1, -3).
10. Suppose that T R R is a linear transformation with T(1,0.1 1,2,0,1).
T(1,1,0)-(2,1,1.0),
T(0,1,0)-(1-2,1,1) Find the standard matrix for T.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed180457-2ca6-4012-a54e-e269d4f35cc4%2F7a8db55b-ed26-4bcd-a94d-09c919ec7908%2F66hp0ys_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Consider a matrix A=
8.
Find the characteristic equation of the matrix A, and then find the eigenvalues and
cigenvectors.
4. Find the standard matrix for T where Tryr,)3(2x,+ -2r,).
5. Consider a linear transfomation T R- R which refects a vector about the line
y--r. and dilates the reflected vector by a factor of 2. Find the standard matrix for
the linear transformation.
[102]
6 Find the kemnel of the linear transformation whose standard matnx is B-215
[237]
7. Consider the transformation tw 5r,-3r, w, =2r, +a, Detemmine whether the
transformation is one-to-one.
8 Find the canonical basis for the solution space of the homogeneous system.
+2,+ + =0
2+5,+3r,+2x,0
2+3+2,+ ,=0
9. Find a basis for the hyperplane a where aF2,1, -3).
10. Suppose that T R R is a linear transformation with T(1,0.1 1,2,0,1).
T(1,1,0)-(2,1,1.0),
T(0,1,0)-(1-2,1,1) Find the standard matrix for T.
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