MTH501 Quiz 4 by VU Topper RM

If the augmented matrices of two linear systems are row equivalent, then the two systems have the ______ solution set.

A. same

B. different C. inconsistant D. trivial

A m ×n matrix U has orthonormal columns if and only if UT U = I

True

False

Lets={u1+u2+......up}be the set of non-zero vectors in Rnis said to be an orthogonal set if all vectors in S are mutually orthogonal. That is O∉ S andui.uj=0∀ i≠ j, i,j=1,2,……..p.

True

False

If x is orthogonal to both u and v, then x must be _______ to u – v. A. orthonormal

B. orthogonal

C. equal D. parallel

If u=(1, k, 0) and v=(1, 1, 0) are orthogonal vectors then which of the following is the value of k?

1. k = 1
2. k = -1
3. k = 2
4. k = 0

Correct answer: k = -1

A vector whose length is 1 is called -----------

Unit Vector

Identity Vector

Two vectors are _______if at least one of the vector is a multiple of the other

If B= is an orthogonal set of vectors with respect to an inner product on a vector space V, then the set B A. Is an orthonormal basis for v B. Is linearly independent. C. Spans the vector space v D. Linearly dependent.

If u=(2, 0, -1) and v=(0, -1, 0) is an orthogonal set then which of the following has a norm of 1?

1. v.u
2. u.u
3. v.v
4. u.v

Correct answer: v.v

If u and v are vectors in Rn, then we regard u and v as n×1 matrices. The matrix product utv is a ----------- matrix. A. n × 1

B. n × n

C. 1 × n D. 1 × 1

7x + 2y = 16 –21x – 6y = 24 The above system has a ___________ solution. A. unique B. consistent

C. inconsistent

D. trivial

The process of creating the unit vector u from v sometime called-------- Diagonalizing v

Normalizing v

For u, v vectors in , the distance between u and v is written as Rn

A. dist(u, v) = ||u − v||

B. dist(u, v) = ||v − v|| C. dist(u, v) = ||u − u|| D. None of these

Suppose x,y,z are some vectors in an inner product space (v,<,>) such that <x,y>=<x,z> for all x∈V, then y=z

True

False

If we divide a non-zero vector by its length we get a A. zero vector

B. unit vector

C. normalized vector D. none of these

The matrix A^T(Transpose of A) x A is ________ if and only if the

A. symmetric

B. invertible

C. singular D. scalar