Augment the following matrix with the identity then find its inverse. $$A = \begin{bmatrix}&2 &1 & 6 \\&2 & 0 & 6 \\& 3 & 4 & -1\end{bmatrix}$$

Parts a) and b) of this problem are independent. a) Let $$H = \{\begin{bmatrix}& a + 3b -5c \\& -a -3b + c \\& 2a +6b – 2c\end{bmatrix} : a, b, c \in \mathbb{R} \}$$. i) Prove that H is a subspace. Hint: using a theorem is faster than using the definition of a subspace. ii) Find a basis for H.   b) Let $$A = \begin{bmatrix}&2 &2 & 1 \\&1 & 0 & 1 \\& -1 & 2 & -1\end{bmatrix}$$ Find the second column of the inverse of A without computing $$A^{-1}$$.

Which division of the nervous system includes the brain and the spinal cord?

The wide band of white matter that connects the left and right cerebral hemispheres is the:

 In negative feedback, a rising hormone level typically:

The three connective-tissue membranes that cover and protect the brain and spinal cord are the:

A boat is pulled toward a dock by a rope from the bow through a ring on the dock 9 feet above the bow. The rope is hauled in at a rate of 5 feet per second. At what rate is the distance between the boat and the dock changing when 41 feet of rope are out? Use the math editor (“Insert Math Equation” as needed on the toolbar) to enter your final answer. Show all work on your paper.

Use Calculus to find the solutions. Justify your solution by using Calculus techniques. Use the math editor (“Insert Math Equation” as needed on the toolbar) to enter your final answer. Show all work on your paper. Make sure to label your answers.   Find two numbers such that the difference of the first and eight times the second number is -240 that yield the minimum product.  

When Pr(US|CS) < Pr(US|no CS), a _____________ contingency exists between the CS and US.

What do we observe if a CS passes the summation test?