(1) Let T: P→ Py be a linear transformation such that T(ar²+bx+c) = (a-3b)z²+z+2c. Then a basis for Ker(T)-Z(T) = Nul(T) is (a) (3x + 1) (33²+z) (ii) Let T as above. Then a basis for the Range(T) is (a) (x²-3x, 1) (c) {z²-3) (d) (², 1) (iii) Consider the integral inner product on P₁, where a = 0 and b= 1. The distance between fi(x) = z²+3x+1 and f(x)=x²+1 (a) 9 (0) 73 A is not diagnolizable A is diagnolizable (2², 2+2) (c) {z², z) (c) 3 (d) 4.5 (iv) Let T: PP, such that 7(ar²+bx+c) = (4a+b+c)² +5bx+Se. Then 5 is an eigenvalue of T. Hence Es= 6) span(x² + x, 3² +1} (vi) Given D= (b) span (²-1) (c) span {²+x+1} (d) span(1,2) (v) Let A be a 3 x 3 matrix such that Ca(a) = (a-2)²(a-3). Given Espan{(1,0,0)) and Es span ((0,2,2)). One of the following statements is true (b) It is possible that A-¹ does not exist اکاری (d) {-3x+1} Habe R ( ] [ ] 169 41616161 (Ⓒ) { (c) Trace(A) = 5 R) is a subspace of R²x2. Then a basis for Dis DE 2) 11 (d)
(1) Let T: P→ Py be a linear transformation such that T(ar²+bx+c) = (a-3b)z²+z+2c. Then a basis for Ker(T)-Z(T) = Nul(T) is (a) (3x + 1) (33²+z) (ii) Let T as above. Then a basis for the Range(T) is (a) (x²-3x, 1) (c) {z²-3) (d) (², 1) (iii) Consider the integral inner product on P₁, where a = 0 and b= 1. The distance between fi(x) = z²+3x+1 and f(x)=x²+1 (a) 9 (0) 73 A is not diagnolizable A is diagnolizable (2², 2+2) (c) {z², z) (c) 3 (d) 4.5 (iv) Let T: PP, such that 7(ar²+bx+c) = (4a+b+c)² +5bx+Se. Then 5 is an eigenvalue of T. Hence Es= 6) span(x² + x, 3² +1} (vi) Given D= (b) span (²-1) (c) span {²+x+1} (d) span(1,2) (v) Let A be a 3 x 3 matrix such that Ca(a) = (a-2)²(a-3). Given Espan{(1,0,0)) and Es span ((0,2,2)). One of the following statements is true (b) It is possible that A-¹ does not exist اکاری (d) {-3x+1} Habe R ( ] [ ] 169 41616161 (Ⓒ) { (c) Trace(A) = 5 R) is a subspace of R²x2. Then a basis for Dis DE 2) 11 (d)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![(1) Let T: P→ Py be a linear transformation such that T(ar²+bx+c)=(a-3b)x² + cz +2c. Then a basis
for Ker(T)-Z(T) = Nul(T) is
(a) (3x + 1}
(3x² + z}
(ii) Let T as above. Then a basis for the Range(T) is
(a) (x²-3x, 1}
(c) {z²-3)
(d) (², 1)
(iii) Consider the integral inner product on P, where a = 0 and b= 1. The distance between fi(x)=x²+3x+1
and f(x)=x²+1
(a) 9
0573 (c) 3
A is not diagnolizable
A-¹ is diagnolizable
(vi) Given D= {]
(2², 2+2) (c) (z², x)
(iv) Let T: PP, such that 7(ar²+bx+c) = (4a + b + c)² +5bx+Sc. Then 5 is an eigenvalue of 7.
Hence Es=
62) span(2² + x, 3² + 1}
کو
(b) span (²-1) (c) span (²+2+1} (d) span(1,2)
(v) Let A be a 3 x 3 matrix such that Ca(a)= (a-2)²(a-3). Given Espan{(1,0,0)) and Es
span((0,2,2)). One of the following statements is true
(b) It is possible that A-¹ does not exist
(d) 4.5
169
(d) {-3x+1}
Habe
a,be R) is a subspace of R2x2. Then a basis for Dis
11
(c) Trace(A) = 5
****](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F43db1c21-26d3-473a-8503-cd8e5f43a3f8%2F9ce5beb6-0d15-4814-8d96-d8d402c0a10b%2Fci6ka4p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(1) Let T: P→ Py be a linear transformation such that T(ar²+bx+c)=(a-3b)x² + cz +2c. Then a basis
for Ker(T)-Z(T) = Nul(T) is
(a) (3x + 1}
(3x² + z}
(ii) Let T as above. Then a basis for the Range(T) is
(a) (x²-3x, 1}
(c) {z²-3)
(d) (², 1)
(iii) Consider the integral inner product on P, where a = 0 and b= 1. The distance between fi(x)=x²+3x+1
and f(x)=x²+1
(a) 9
0573 (c) 3
A is not diagnolizable
A-¹ is diagnolizable
(vi) Given D= {]
(2², 2+2) (c) (z², x)
(iv) Let T: PP, such that 7(ar²+bx+c) = (4a + b + c)² +5bx+Sc. Then 5 is an eigenvalue of 7.
Hence Es=
62) span(2² + x, 3² + 1}
کو
(b) span (²-1) (c) span (²+2+1} (d) span(1,2)
(v) Let A be a 3 x 3 matrix such that Ca(a)= (a-2)²(a-3). Given Espan{(1,0,0)) and Es
span((0,2,2)). One of the following statements is true
(b) It is possible that A-¹ does not exist
(d) 4.5
169
(d) {-3x+1}
Habe
a,be R) is a subspace of R2x2. Then a basis for Dis
11
(c) Trace(A) = 5
****
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
