Matrix Multiplication & Network Applications (Year 11)
Free printable Year 11 General Mathematics worksheet on matrix multiplication, the order of a product, and using the square of a link matrix to count two-step routes (ACMGM015-016).
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Year 11 · Math worksheet
Name
Date
Math
Matrices: Multiplication and Network Applications
State the order of each product (or whether it can be formed), compute each matrix product, or use the square of a link matrix to count two-step routes.
- 1.Matrix A has order 3 x 4 and matrix B has order 4 x 2. State the order of the product AB.
- 2.Matrix A has order 3 x 3 and matrix B has order 3 x 3. State the order of the product AB.
- 3.Matrix A has order 2 x 3 and matrix B has order 4 x 2. Can the product AB be formed? If so, state its order.
- 4.Find the matrix product AB, where A = [2 5; 3 6] and B = [3 2; 2 5].
- 5.Find the matrix product AB, where A = [2 3; 1 2] and B = [4; 3].
- 6.Find the matrix product AB, where A = [6 2 5; 2 6 4] and B = [2; 3; 3].
- 7.The matrix M = [0 1 1; 1 0 0; 1 0 0] records direct one-step links between towns P, Q and R (a 1 means a direct road, rows and columns in the order P, Q, R). The number of different two-step routes from Q to R (via exactly one other town) is the entry of in row 2, column 3. Find that number.
- 8.The matrix M = [0 0 1; 0 0 1; 1 1 0] records direct one-step links between towns P, Q and R (a 1 means a direct road, rows and columns in the order P, Q, R). The number of different two-step routes from Q to P (via exactly one other town) is the entry of in row 2, column 1. Find that number.
- 9.The matrix M = [0 1 1; 1 0 1; 1 1 0] records direct one-step links between towns P, Q and R (a 1 means a direct road, rows and columns in the order P, Q, R). The number of different two-step routes from R to Q (via exactly one other town) is the entry of in row 3, column 2. Find that number.
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