Linear Algebra

1.V is a set of solution of differential equation d²y/dx²-5dy/dx+6y=0 . also v(F) is a bounded set of solutions. Then

|V|=?

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2.V is a set of m*n matrices with rational entries. Then V is a vector space over R or not..

• V is not a vector space over R

• V is a vector space over R

3.V is a set of m×n matrices with R entries. Then V is a vector space over Q or not..

• V is not a vector space over Q

• V is a vector space over Q

4.Choose the incorrect statement ..

V(F) is a vector space over field F. then

• if F=Q then V(Q) is called Rational vector space

• if F=R then V(R) is called Real vector space

• F=N then V(N) is called natural vector space

• if F=C then V(C) is called complex vector space

5.Dim[c³(c)]=…………….

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6.Dim[cⁿ(R)]=………………

• n, ∀n∈N

• n+1, ∀n∈N

• 3n, ∀n∈N

• 2n , ∀n∊N

W⊆R³(R) and defined as W={(a,b,c); a+b+c=0} then find

dim[ W(R)]..

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A linear transformation T:U(F)→V(F) is called linear operation when………….

• domain≠co-domain

• domain=co-domain

Find ∥(1+I,2-i)∥

• √2+5

• 2+√5

• √2+√5

• √7

Tags

CCSS.HSN.CN.B.6

What is schwartz’s inequality

• ∣α,β∣ ≥ ∥α∥∥β∥

• ∣α,β∣ ≤ ∥α∥∥β∥

• ∣α,β∣ ≥ ∥α∥+∥β∥

• ∣α,β∣ ≤ ∥α∥+∥β∥