xample: Solving Axb, Ux = c, and Rx = d 1x1 + 2x2 + 3x3 + 5x4 Ax=b is 2x₁ + 4x2 + 8x3 + 12x4 = 3x₁ + 6x2 + 7x3 + 13x4 = 4- bi b2 b3 1. Reduce [A b] to [U c], to reach a triangular system Ux = c. 2. Find the condition on b₁, b₂, b3 to have a solution. 3. Describe the column space of 4: Which plane in R³? 4. Describe the nullspace of A: Which special solutions in R4? 5. Find a particular solution to Ax=(0;6;-6) and the complete x+x. 6. Reduce [Uc] to [R d]: Special solutions from R and. Xp from d.

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.