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  • Perplex
    IB Math AIHL
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    Matrices
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    Problems

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    Problem Bank - Matrices

    Access custom-built, exam-style problems for matrices. Each problem has a full solution and mark-scheme, as well as AI grading and support.

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    IB: 4
    1

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    The matrix below shows the selling price (in USD) of three snack packs S1​,S2​ and S3​ at two vending machines A and B.

    S1​​S2​​S3​​
    AB​(1.201.30​1.751.60​2.001.90​)

    A student club places an order of 50 of S1​, 80 of S2​, and 40 of S3​.

    1. Write down a matrix equation for the total revenue vector R (2×1) from each machine.

      [2]
    2. Hence calculate the total revenue from vending‑machine A and from vending‑machine B.

      [3]
    2

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    The regional sales of three products A, B and C by two branches, North and South, are given (in units) by the matrix

    Q=(10080​75120​5090​)

    where the first row is North and the second is South. The shipping rate (in $USD per unit) charged by Carrier 1 and Carrier 2 for each product is

    S=⎝⎛​0.500.600.75​0.650.550.70​⎠⎞​

    where rows correspond to products A, B, and C and columns to Carriers 1 and 2 respectively.

    1. Write down a matrix equation for the total shipping‑cost matrix C, and hence find C.

      [2]
    2. For each branch, state which carrier is cheapest.

      [3]
    3

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    0 / 8

    The number of tilapia, catfish and trout harvested (in units) by Farm A and Farm B during a season is given by the matrix

    H=(220200​180190​140150​)

    where the first row is Farm A and the second is Farm B. Each fish species has an average weight (kg) and a selling price (USD) per fish, as shown by

    F=⎝⎛​0.400.600.50​6.007.508.00​⎠⎞​

    where rows correspond to tilapia, catfish and trout, and columns correspond to weight and price respectively.

    1. Find the total weight–revenue matrix T.

      [2]
    2. For each farm, determine

      1. the total weight harvested (kg);

        [2]
      2. the total revenue earned (USD);

        [2]
    3. Hence state which farm has the higher revenue per kg.

      [2]
    4

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    A system of equations is given by

    ⎩⎪⎪⎪⎨⎪⎪⎪⎧​x+2y+z=4,2x+y+3z=9,x+0y+2z=5.​
    1. Write this system in the form Ax=b, and find A−1.

      [3]
    2. Hence solve for (x,y,z).

      [2]
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