Linear Algebra Answers

Clara invests $5000 in an account that pays 6.25% per year. How much will she have after 15 years? If the interest was compounded quarterly, how much would she have?

A city population has been increasing 3% each year. If the initial population was 15,500, write the exponential function then determine how many people there are after 12 years?

Tony purchased a rare 1959 Gibson Les Paul guitar in 2000 for $12,000. Experts estimate that its value appreciates by 14% per year. Write the exponential function then determine its value today (2018).

Mr. Akpalu went to a market to purchase 3 kg of sugar, 10 kg of wheat and 1 kg of salt. In a shop near to Mr. Akpalu’s residence, these commodities are priced at € 20, €10 and € 6 per kg whereas in the local market these commodities are priced at € 15, € 8 and € 6 per kg respectively. If the cost of traveling to local market is € 25, find the net savings of Mr. Akpalu, using matrix multiplication method.

Show that T:R^3 →R^2: T(x,y,z)= (2x+y-z,x+z) is a linear transformation. Verify that T satisfies the Rank-nullity theorem

Express v=(2,-5,3) in R³ as a linear combination of the vectors U₁ =(1,-3,2) , U₂=(2,-4,-1), U₃ =(1,-5,7)

Consider the subspace U of R⁴ spanned by the vectors.

V₁ =(1,1,1,1), V₂= (1,1,2,4 ), V₃= (1,2,-4,-3)

Find

1) an orthogonal bassis of V.

2) an orthogonal basis of V.

Show that the vectors u₁ =(1,1,1), u₂ =(1,2,3), u₃ 3=(1,5,8) span R²

Check whether or not * is a binary operation on S={x∈R| x>0}, where x*y=| In(xy)|