There is no new mathematics material this week. You will be required to use Excel to do matrix calculations and solve linear systems of equations in Excel HW #2. We provide Excel Tutorials to help you.
An array is the same as a matrix: a rectangular block of numbers. Mathematicians call it matrix, computer scientists call it array.
An array formula in Excel is a formula that returns a matrix as a result. The array formulas we use in this class are
You enter array formulas the same way you enter other formulas, except for two things:
If you forget either one of those things, there is nothing you can do except start over with entering the formula.
Example: Suppose you want to multiply a 2x2 matrix A, stored in A1:B2, with a 2x2 matrix B stored in D1:E2. You want to store the result in G1:H2. You need to do the following:
Caution: Excel lets you calculate =A1:B2*D1:E2, but that is not the matrix product. That is the element-by-element product (C11 = A11*B11, instead of C11 = A11*B11+A12*B21).
Example: Suppose you want to compute 2A+3B instead, and store it in G1:H2 again. You do the following:
Example: Suppose you want to find the inverse of a 3x3 matrix A stored in A1:C3. (You can only find the inverse of a square matrix). The inverse is again of size 3x3.
A system of linear equations is written in matrix notation as Ax=b. A is the matrix of coefficients, x is the vector of unknowns, b is the vector of right-hand sides. Formally, the solution is x = A-1*b. That is the way Excel solves equations.
Suppose you want to solve the system
3x + 4y = 1
x - 2y = 7
You type in the matrix somewhere (for example in A2:B3), likewise for the right-hand side (for example in D2:D3). Then you need to
The result (3,-2) shows up in F2:F3.
Note: a couple of the problems say "solve by Gauss-Jordan Elimination". Just ignore that, and solve the equations by whatever method you prefer.