MTH501 Quiz 4 January 2026 Set 2

Question:

Let WWW is a finite dimensional subspace of an inner product space VVV and yyy is any vector in VVV. The best approximation to yyy from WWW is then

A. ProjwyProjywProj^{w}_{y} B. ProjywProjwyProj^{y}_{w} Copied: 1/8/2026, 10:49:34 PM

Question:

Which of the following set of vectors is an orthogonal set?

1. (1, 1, 1) ;( 1, 0,-1)
2. (0, 1, 1) ;( 1, 0,-1)
3. (1, 1, 0) ;( 1, 0,-1)
4. (1, 0, 1) ;( -1, 0, -1)

Correct answer: (1, 1, 1) ;( 1, 0,-1)

Copied: 1/8/2026, 10:49:48 PM

Question:

Let s={u1+u2+......up}s={u1+u2+......up}s = \{ {u_1} + {u_2} + ......{u_p}\} be a basis for a subspace W of RnRn{R^n} , is also an orthogonal basis if S is an orthogonal set.

A. False

Question:

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

A. orthogonal

B. equal C. parallel D. orthonormal Copied: 1/8/2026, 10:50:59 PM

Question:

If two rows are orthogonal, they are __________.

A. linearly dependent

B. linearly independent

Copied: 1/8/2026, 10:51:12 PM

Question:

If B={v1,v2,v3}{v1,v2,v3}\{ {v_1},{v_2},{v_3}\} is an orthogonal set of vectors with respect to an inner product on a vector space V, then the set B

A. Is linearly independent. B. Linearly dependent.

C. Spans the vector space v

D. Is an orthonormal basis for v Copied: 1/8/2026, 10:51:24 PM

Question:

If a square matrix has __________ columns, then it also has orthonormal rows.

A. orthonormal

B. orthogonal Copied: 1/8/2026, 10:51:37 PM

Question:

Elementary row operations on a matrix do not affect the -------- relations among the columns of the matrix.

A. Linear independence

B. Linear dependence

Copied: 1/8/2026, 10:51:54 PM