Write v as the sum of two vectors, one in Span fu,} and one in Span fu2,u3,u4}. Assume that fu1 .u4} is an orthogonal basis for R*. ..... - 5 - 1 5 3 5 U2 = 5 u4 - 5 8 u = - 1 Uz = 5 4 - 5 - 1

Q: 4. Express PQ-RQ+SR-PS+RS as a single vector.

A: Expression

Q: Assume that A is row equivalent to B. Find bases for Nul A and Col A. - 2 8 -2 - 8 10 8 11 A = 2 -…

A: The null space of any matrix A consists of all the vectors B such that AB = 0 and B is not zero

Q: Let v1, v2, v3 be the vectors in R^3 defined by: v1=[0 5 8], v2=[12,-20,5], v3=[-12,15,-13] a). Is…

A: Solution: (a) We see,            v1 + v2 = [0 5 8] + [12 -20 5]                          = [0+12…

Q: Let a = (-4, 3, 4) and b = (-5, 2, 3), then find the decomposition a = a +a of a with respect to b a…

A: Ggg

Q: Which matrix could be used to rotate a vector 64 degrees clockwise about the origin? cos (-64) sin…

A: we have to find  matrix could be used to rotate a vector 64 degrees clockwise about the origin.

Q: If the cross product of two nonzero vectors is the zero vector, then each of the two vectors is a…

A: Explanation of the answer is as follows

Q: vecterd (l,l.3) .c2.3.6] a (libis) form Do the budia fer R?

A:

Q: Let e1, e2, e3, e4, ē5, e6} be the standard basis in R°. Find the length of the vector * = 471+…

A:

Q: Decide whether the vectors [2, 9, -1, 4, 7, 8, 10, 9], [11, 2, 5, -9, 0, 0, -1, 3], [4, 18, -2, 8,…

A: We have to decide whether the given vectors are linearly independent. Then, we can proceed further.

Q: Is it true that there is a basis for R^4 that consists of five vectors?

A: False. First I recall you what is the definition of basis. set B of vectors in a vector space V is…

Q: Find a non-zero vector perpendicular to

A:

Q: Which of the following sets of vectors spans R^2?  A. {(1, 1), (–2, –2)} B. {(1, 1), (1, 2)} C.…

A:

Q: 3) Let C be a basis that contains vectors (−2 + 1x + 1x2 + (−1) x3), (1 + (−2) x + 4x2 + 2x3), (−2 +…

A:

Q: The vectors (attached) form a basis of R^3 (R = Real numbers) if and only if k does not equal blank

A: