Final Written Assessment

$\ln(ab)=\ln a + \ln b$

$\ln(ab)=\ln a \cdot \ln b$

$\ln(a+b)=\ln a + \ln b$

$\ln(a/b)=\ln a / \ln b$

$6$

$12$

$9$

$18$

$x>1$

$x\ge 1$

$x>0$

all real $x$

$(0,1)$

$[0,1]$

$(-1,1)$

$(0,\infty)$

$32$

$21$

$(4,10,18)$

$14$

$0$

$1$

$-1$

undefined

$4\times 5$

$3\times 3$

$5\times 4$

undefined — the shapes do not match

$A$ is invertible (full rank)

$\operatorname{rank}(A)<3$ and $b$ lies in the column space of $A$

$b=0$ and $A$ is invertible

$\operatorname{rank}(A)=3$ and $b\neq 0$

$90\%$

$50\%$

$81\%$

$10\%$

$0$

$3$

undefined

$\infty$

$12x^3$

$3x^3$

$12x^4$

$4x^3$

$(3,\ 2y)$

$(3,\ y^2)$

$(3x,\ 2y)$

$3+2y$

$\theta \leftarrow \theta - \eta\,\nabla_\theta L$

$\theta \leftarrow \theta + \eta\,\nabla_\theta L$

$\theta \leftarrow \eta\,\nabla_\theta L$

$\theta \leftarrow \theta - \nabla_\theta L / \eta$

$(3,4)$

$(3,1)$

$(1,4)$

error — the shapes are incompatible