How do you represent a system of linear equations as a matrix product Ax=b?
Conditions
- The system is linear.
- Dimensions of the coefficient matrix, variable vector, and constant vector are compatible.
Reasoning, step by step
- Construct matrix A where each row contains the coefficients of the variables for one equation.
- Construct vector x listing the unknown variables.
- Construct vector b listing the constant terms from the right-hand side of each equation.
- Ensure the dimensions of A, x, and b align for matrix multiplication.
Example
The script states: 'In Ax=b, rows of A contain the equation coefficients, x lists the unknowns, and b lists the constants. The dimensions must match.'
Common misconceptions
- Placing constants in matrix A instead of vector b.
- Ignoring dimension mismatches between the number of equations and variables.
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