Day 5 Outline

Homework return quandry

Returning graded homeworks to 90 students during class will take a large chunk of time ...

Idea: QR-coded blank sheets

You would write all your answers on copies of this sheet, then I could automatically email your graded homework back to you. Would require single-sided and no staples so that papers can be easily scanned.

Applications (1.6 & 1.10)

1.10.5 Loop currents

Solve for the loop currents


Peanut butter sandwich

Peanut butter sandwich review

1.7 Linear independence

Def: LI and LD. LDR.

Little new here: we already know to look at RE form of matrix whose columns are the vectors.

A few examples of LI and LD sets.

Exercise 1.7.42: selecting columns from a matrix ("slicing").

Thm 8. (wide)

Thm 9. (inclusion of zero vector)

1.8 Linear transformations

Def of LT as function with 2 properties.


Specified by action on standard unit vectors.

Equal to L(x) = Ax where columns of A are images of standard unit vectors.

Examples using illustration of transformations R2 to R2:

  • projection in 3d
  • shear
  • reflection
  • dilation
  • rotation

Domain, codomain, range

1-1 and onto

Theorem 11: T 1-1 iff T(x)=0 has only trivial solution.

Theorem 12: T from Rm to Rn and A its standard matrix. T 1-1 iff columns of A are LI.

1.10 Migration

City - burbs

Set up matrix