(a) Every vector of R² is a linear combination of the vectors (-2,3),(1, 1) and (4,1)?(b) Is every vector in R³a linear combination of the vectors (-2, 1, 3) and (3, 2, 1)?(c) The Vector (2, –1,2) belong to the subspace generated by vectors (3,2, -1) and(-3,0,2}?

Answered: (a) Every vector of R² is a linear…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Find a basis for the subspace of R° that is spanned by the vectors V1 = (1, 0, 0), v2 = (1, 0, 1), v3 = (5, 0, 1), v4 = (0, 0, -2) V2 and v4 form a basis for span {v1, V2, V3, V4}. V1 and v4 form a basis for span {v1, V2, V3, V4}. V1 and v3 form a basis for span {v1, V2, V3, V4}. Ov1 and v2 form a basis for span {v1, V2, V3, V4}. V2 and v3 form a basis for span {v1, V2, V3, V4}. V3 and v4 form a basis for span {v1, V2, V3, V4}.
Let H span {(0,-1,-2), (-2, -4, 1), (3, 3, -1)}. A basis for the subspace HCR³ is { 2. }. vector
Suppose that V is a that has subspaces of U and W. Furthermore, suppose that {u¹, u2} is a basis for U, that {1, 2} is a basis for W and that the only vector that U and W have in common is the zero vector 0. Show that {u¹, u², w¹, w²}. After you get done, note where you used the fact that the only vector common to both U and W is 0. (Without this condition the vectors {u¹, u², w², w2} don't need to be linearly independent, so if you didn't use this condition you definitely made a mistake somewhere.)
Find a basis of the subspace of R' defined by the equation -5x1- 5x2+ 2x3 = 0. Basis:
The set of vectors {(1,1,0,0),(0,-1,0,0),(0,0,1,1),(1,0,1,1)} is linearly dependent. What is a valid expression of the last vector as a linear combination of the others? a. (1,0,1,1)=(1,1,0,0)+(0,-1,0,0)-(0,0,1,1) b. (1,0,1,1)=(1,1,0,0)+(0,-1,0,0)+(0,0,1,1) c. (1,0,1,1)=-(1,1,0,0)+(0,-1,0,0)+(0,0,1,1) d. (1,0,1,1)=2(1,1,0,0)+2(0,-1,0,0)+2(0,0,1,1)
I know the basis converted to orthogonal is {<2, 1, -1, 1>,<11, -12, 5, -5>,<-1, -3, 0, 5>} and that the magnitude of these will be sqrt(7), sqrt(315), sqrt(35) - but I'm not sure how to use these to convert the basis to orthonormal.
3) Find a basis of F3 containing the vectors (1, 2, -3), (2, 6, -3)
2 0 1 4 5 30x3 = 43 = (25² 0 ..] Can we use Cramer's Rule to check if the column vectors of A are linearly (in)dependent? Explain why or why not and regardless, identify all linearly independent column vectors in A. *Derive the vector x3 in Ax3 = b by two different methods (please show the essential calculations- outlining the method(s) isn't enough to get you credit).

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,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS

(a) Every vector of R² is a linear combination of the vectors (-2,3), (1, 1) and (4,1)? (b) Is every vector in IR³ linear combination of the vectors (-2, 1, 3) and (3, 2, 1)? (c) The Vector (2, –1, 2) belong to the subspace generated by vectors (3,2, -1) and (-3,0,2}?