Sec 3 E-Math Matrices topical questions

For the matrix M = [[4, 7, 2], [9, 1, 6]], state (a) the order of M and (b) the element m₂₁.

Given A = [[3, −1], [0, 5]] and B = [[1, 4], [−2, 2]], find A + B.

Find 2A − B where A = [[5, 2], [1, 0]] and B = [[1, 2], [3, 4]].

A bakery’s weekly sales are given by S = [[18, 25], [30, 12]], where rows are the two branches and columns are plain and chocolate cakes. Find the matrix for four identical weeks.

Given M = [[2, 1], [0, 3]], find M².

Find the product [[1, 2, 3], [4, 5, 6]] × [[7, 8], [9, 10], [11, 12]].

A has order 3 × 2 and B has order 2 × 4. (a) State whether AB is defined and, if so, its order. (b) State whether BA is defined, with a reason.

A shop’s monthly sales are Q = [[15, 20], [10, 25]] (rows = two outlets; columns = two products) and the prices are P = [[3], [5]] per unit. (a) Find QP. (b) Interpret both entries of your answer.

Matrices A and B satisfy A + B = [[6, 10], [5, 8]], where A = [[7, 3], [4, 4]] and B = [[2, x], [1, y]]. (a) Form equations for x and y. (b) Solve them. (c) Verify the remaining entries of the sum.

Let A = [[5, 2], [1, 3]], 0 denote the 2 × 2 zero matrix and I the 2 × 2 identity matrix. Find (a) AI, (b) A + 0, and (c) explain what multiplying A by the zero matrix gives and why.

1. (a)AI.[1]
2. (b)A + 0.[1]
3. (c)A × zero matrix, with a reason.[2]

A bakery sells plain cakes at $4 and chocolate cakes at $7. Weekend sales are S = [[12, 8], [15, 10]] (rows = weekend 1, weekend 2; columns = plain, chocolate). (a) Find SP where P = [[4], [7]]. (b) Find the total revenue over both weekends. (c) Which weekend earned more, and by how much?

A = [[2, 1], [0, x]] and B = [[1, 2], [3, 1]]. (a) Show that AB = [[5, 5], [3x, x]]. (b) Given that AB = [[5, 5], [6, 2]], find x and verify it satisfies both bottom entries.

A = [[1, 2], [3, 4]] and B = [[2, 0], [1, 3]]. (a) Find 2A + B. (b) Find AB. (c) Determine whether BA = AB, supporting your answer with a calculation.

A stationer’s stock is S = [[10, 5, 8], [6, 9, 4]] (rows = two branches; columns = pens, notebooks, files) and a delivery adds R = [[4, 2, 1], [3, 1, 5]]. Prices per item are P = [[2], [3], [1]]. (a) Find S + R. (b) Use a matrix product to find the value of stock at each branch after the delivery. (c) State which branch holds the more valuable stock.

1. (a)Find S + R.[2]
2. (b)Find the stock values.[3]
3. (c)Compare the branches.[1]

A bakery’s weekend sales matrix is Q = [[40, 25, 30], [55, 20, 35]] (rows = Saturday, Sunday; columns = loaves, buns, cakes) and the price column is p = [[2], [3], [1]] in dollars. (a) Find the revenue matrix Qp. (b) All prices rise by 10% on Monday. Write the new revenue matrix, using a scalar multiple. (c) State the total weekend revenue before and after the rise.

1. (a)Find Qp.[2]
2. (b)New revenue matrix.[2]
3. (c)Weekend totals before and after.[2]