2. (a) Let L2×2 denote vector space of all 2 × 2 lower triangular real matrices. Determine if B = 1 0 2 3 , 2 0 −2 1 , −2 0 −2 −2 forms a basis for L2×2. (b) Let U2×2 denote vector space of all 2 × 2 upper triangular real matrices. Determine if B = 1 2 0 3 , 2 2 0 1 , −1 0 0 2 forms a basis for U2×2.

the correct answer is 5 6 and 7

(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

  a₁ = $ 30 000

  r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.

when the daily mileage is greater than 40 miles, unlimited mileage plan will save you money. 40 miles is the break-even point.

step-by-step explanation: