Let -4 M = 3 be a vector in the vector space V of 2 × 2 matrices with real number entries. Let B be an ordered basis for V. 0 0 0 0 0 = { [ ] [ ] [ ] [ ] } a. Write M as a linear combination of elements of B. 4 = 3 -1 [10] 00 Го + + Го 07 10 ] Го + b. Let [M]B denote the coordinate representation of M relative to the basis B. Find the coordinate vector representation for M relative to the basis B. Your answer should be a vector of the general form <1,2,3,4>. [M]B=
Let -4 M = 3 be a vector in the vector space V of 2 × 2 matrices with real number entries. Let B be an ordered basis for V. 0 0 0 0 0 = { [ ] [ ] [ ] [ ] } a. Write M as a linear combination of elements of B. 4 = 3 -1 [10] 00 Го + + Го 07 10 ] Го + b. Let [M]B denote the coordinate representation of M relative to the basis B. Find the coordinate vector representation for M relative to the basis B. Your answer should be a vector of the general form <1,2,3,4>. [M]B=
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
100%
![Let
-4
M =
3
be a vector in the vector space V of 2 × 2 matrices with real number entries. Let
B
be an ordered basis for V.
0 0 0 0 0
= { [ ] [ ] [ ] [ ] }
a. Write M as a linear combination of elements of B.
4
=
3
-1
[10]
00
Го
+
+
Го 07
10
]
Го
+
b. Let [M]B denote the coordinate representation of M relative to the basis B. Find
the coordinate vector representation for M relative to the basis B. Your answer
should be a vector of the general form <1,2,3,4>.
[M]B=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5f3a7f3-10c4-4869-906a-40675d8d17a6%2F8a3e3119-1f7f-4d3c-82d8-a08e649aca70%2Fu8p0p9r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let
-4
M =
3
be a vector in the vector space V of 2 × 2 matrices with real number entries. Let
B
be an ordered basis for V.
0 0 0 0 0
= { [ ] [ ] [ ] [ ] }
a. Write M as a linear combination of elements of B.
4
=
3
-1
[10]
00
Го
+
+
Го 07
10
]
Го
+
b. Let [M]B denote the coordinate representation of M relative to the basis B. Find
the coordinate vector representation for M relative to the basis B. Your answer
should be a vector of the general form <1,2,3,4>.
[M]B=
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 1 steps with 2 images
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,
