Linear Algebra 11. True or False. Circle your answer. (a) T F If P is a projecti

Question

Linear Algebra 11. True or False. Circle your answer. (a) T F If P is a projection matrx, then PP. (b) T F: If A is an n × n square matrix, then A (ATA)-1Ar_ In, the n × n identity matrix. (c) T F: If a and b are orthogonal to eachother, then the projection of b on to a is o, the zero vector and the error vector e b. (d) T F: (ATA) is invertible if and only if the columns of A are linearly independent. (e) TF The minimal distance of a vector v from a subspace W is the length of the projection of v onto W. (O) T F: If four vectors in R4 are orthogonal, then they form a basis for R4. (g) T F: Let U and W be two subspaces of a vector space V such that W c U, then W cU (h) T F: Let u L v, then any vector orthogonal to u is orthogonal to any vector orthogonal to v. G) T F: An orthogonal matrix Q is invertible. (j) T F: If Q is orthogonal matrix such that Q8-1, then Q-QT,

Explanation / Answer

if you need any point more explanation then comment below .. i will explain you .. and provide examples so that you clearly understand that point .. okk...

a) true ... projection matrix has P^2 = P .. so P^3 = P

b) true ..

c) true .. projection is zero .. because a.b=0..

d) true ... this is general result ,

e) true . minimal distance is the length of projection

f) false ... orthogonal does not imply that it is basis ...

g) false .. if W is subspace of U then 2nd relation is reverse of the given one

h) false ..

i - true orthogonal matrix is self invertible

j - true .. Q is self nvertible matrix so Q^8 = I & Q^7 = Q..

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.