16A Su22 Final Review

Line Up

100

What are the three conditions for a subset of a vectorspace to be a subspace?

closed under addition, closed under scalar multiplication, contains the 0 vector

200

Is c = g(x), where g(x) is an affine function, a linear equation?

Yes, by definition, g(x) = f(x) + a, for some number a, so the equation is just c-a = f(x), which is a linear equation

300

Sp20 Final 8c

C

400

Fa20 Mt1 Q3c

p = −4, q = −1, r = 7.5

500

Find all possible eigenvalues of A, where A^3 + 3A^2 = -2A

lambda = 0, -1, -2

Shocking Structures

100

To measure the voltage across an element, place a voltmeter in _______ with it. 

parallel

200

What does the circuit model for a capacitive touchscreen being touched look like?

Three capacitors: 1 between finger and top plate, 1 between finger and bottom plate, and one between top plate and bottom plate. With respect to the top and bottom plates, the ones associated with the finger are in series, and their equivalent in parallel with the one between the plates.

300

Sp16 Mt2 Q6a

V_o = -2/11V

400

Resistor Cube

5/6 Ohms

500

Fa19 Final Q7a (modified: find full thevenin circuit)

V_th = 0, R_th = -1kOhms

Most Circles

100

Under what condition does the least squares formula give a unique solution?

Columns of A are linearly independent

200

Fa19 Final Q4c (modified: write out least squares equation)

See board

300

Sp18 Final Q8f (modified: what's one issue)

Issue 1: Colinearity

400

Fa18 Final Q6a

M = [[x_h[0] x_l[0] 0 0] , 

[0 0 x_h[0] x_l[0]]

...]

b = [x_h[1] x_l[1] ... ]^T

500

Sp19 Final Q8c

i,jth entry of C^TC is <c_i, c_j> = c_i^Tc_j = 0 if i != 0 and 1 otherwise, making identity. 

Potpourri

100

How do you find the eigenvalues of a matrix?

set det(A - kI) = 0 and solve for k

200

Linear (In)dependence

Linearly dependent

300

Fa18 Mt1 Q4a

[-2 -2 -1]^T *a

400

Sp16 Mt1 Q9e

(iii)

500

Sp21 Mt2 Q7b

(1+sqrt(3))R