Linear Algebra Answers

3(a) An amount of Rs. 8,000 is distributed into three investments at the rate of 7%, 8% and

9% per annum respectively. The total annual income is Rs. 317.50 and the annual income from

the first investment is Rs. 5 more than the income from the second. Find the amount of each

investment using matrix algebra.

3(b) A wholesaler of pencils charges Rs. 24 per dozen on orders of 50 dozens or less. For

orders in excess of 50 dozens, the price is reduced by 20 paise per dozen in excess of 50 dozens.

Find the size of the order that maximizes his total revenue.

3(c) A computer is purchased for Rs. 50,000. It is estimated to depreciate at 10% per annum

every year. Find its scrap value at the end of 12 years.

Let u=(2,6,-7), v=(-1,-1,8), and 3. If (2, 14, 11)=ku+lv what is the value of l?

Let u=(2,6,-7), v=(-1,-1,8), and 3. If (2, 14, 11)=ku+lv what is the value of l?

Let u=(2,6,-7), v=(-1,-1,8), and 3. If (2, 14, 11)=ku+lv what is the value of l?

Prove that V₁"\\cap" V₂ is a subspace of W if and only if V₁"\\subseteq" V₂ or V₂⊆V₁ in which V₁ and V₂ are subspaces of vector space W.