Suppose that W is a subspace of R" with an orthogonal basis {w₁,..., wp} and suppose that {V₁,..., Va} is the orthogonal basis for W. Which of the following statements is (are) true? O a) {w₁,..., Wp, V₁,..., Va} is an orthogonal set Ob)p+q=n Oc) R" is spanned by the set {w₁,..., Wp, V₁,..., Vq} O d) dimW + dimW¹ = n O All the statements are false O All the statements are true O Statements b, c and d O Statements a, b and c O Statements a, b and d

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Suppose that W is a subspace of R" with an orthogonal basis {w₁,..., wp} and suppose that {v₁,..., vq} is the
orthogonal basis for W. Which of the following statements is (are) true?
O a) {w₁,..., Wp, V₁,..., Va} is an orthogonal set
O b)p+q=n
O c) R is spanned by the set {w₁,..., Wp, V₁,..., Vq}
O d) dimW + dimW¹ = n
O All the statements are false
O All the statements are true
O Statements b, c and d
O Statements a, b and c
O Statements a, b and d
Statements a and b
Transcribed Image Text:Suppose that W is a subspace of R" with an orthogonal basis {w₁,..., wp} and suppose that {v₁,..., vq} is the orthogonal basis for W. Which of the following statements is (are) true? O a) {w₁,..., Wp, V₁,..., Va} is an orthogonal set O b)p+q=n O c) R is spanned by the set {w₁,..., Wp, V₁,..., Vq} O d) dimW + dimW¹ = n O All the statements are false O All the statements are true O Statements b, c and d O Statements a, b and c O Statements a, b and d Statements a and b
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