A man by the name of George Hawkins took his son to Dr. Edward McGee and asked him to operate on his son’s hand.  McGee said his son would be in the hospital for three to four days and that his hand would probably heal a few days later.  The son’s hand did not heal for a month. McGee also told the father, “I guarantee if your son has the operation, his hand will be restored 100%.”  

Pete contracts to buy potatoes from Fred at $.50 per pound.  Fred breaches and does not deliver the potatoes.  In the meantime, the price of potatoes has fallen.  Pete is able to buy them on the open market at half the price.  He is better off than if he were to complete the contract with Fred.  Since Pete suffered only a technical injury, he would not be entitled damages if he sued Fred.

Fred promises to give Jean a unique sculpture in exchange for Jean painting Nick’s house, but instead, Fred sells the sculpture to Cloe before Jean begins the job; this act by Fred constitutes  ________________________ which excuses Jean from performing. Once the sculpture has left Fred’s possession, there is no way that Fred can fulfill the promise to give the sculpture to Jean.  

Dr. Patel just finished an appointment with Horace, who shared he has been suffering from mysterious symptoms that lab reports showed to be a sexually transmitted disease.  Dr. Patel retells Horace’s story during her lunch break in the hospital cafeteria “Can you believe this charmer?  This is Horace Smith’s third STD in the past year!  Avoid him on Tinder.” Which of the following is most accurate based on the facts above?

Let $$B = \{ \vec{b}_1, \vec{b}_2 \}$$ and $$C = \{ \vec{c}_1, \vec{c}_2 \}$$ be bases for a vector space V, and suppose $$\vec{b}_1 = \begin{bmatrix}&2\\&3\end{bmatrix}$$ , $$\vec{b}_2 = \begin{bmatrix}&6\\&7\end{bmatrix} $$, $$\vec{c}_1 =\begin{bmatrix}&2\\&5\end{bmatrix}$$, and $$\vec{c}_2 = \begin{bmatrix}&4\\&2\end{bmatrix}$$.   a) Find the change-of-coordinate matrix from $B$ to $C$.   b) Using part a) Find the change-of-coordinate matrix from C to B.   c) Let $$[\vec{x}]_{C} = \begin{bmatrix}&1\\&\frac{1}{2}\end{bmatrix}$$. Find $$[\vec{x}]_{B}$$.  

Solve the following equation for x: 7x – 6 = 1

The two parts of this problem are independent.   a) Show that if $$||\vec{u}-\vec{v}||^2 = ||\vec{u}+\vec{v}||^2$$ then $$\vec{u}$$ and $$\vec{v}$$ are orthogonal.   b) Let $$\{\vec{u}_1, \vec{u}_2, \vec{u}_3, \vec{u}_4\}$$ be an orthogonal basis for $$R^4$$. Let W be Span $$\{\vec{u}_1, \vec{u}_2, \vec{u}_3\}$$. Write $$\vec{x}$$ as the sum of two vectors, one in W and the other perpendicular to W. $$\vec{u}_1 = \begin{bmatrix}&1 \\&1 \\&0 \\&-1\end{bmatrix}$$, $$\vec{u}_2 = \begin{bmatrix}&1 \\&0 \\&1 \\&1\end{bmatrix}$$, $$\vec{u}_3 = \begin{bmatrix}&0 \\&-1 \\&1 \\&-1\end{bmatrix}$$, and $$\vec{x} = \begin{bmatrix}&-2 \\&3 \\&6 \\&-4\end{bmatrix}$$  

From which country in the world are you taking this course?

Consider $$A = \begin{bmatrix}&8 & 2 & -2 & 0 &5 \\&12 & 3 & -3 & 6 &0 \\&4 & 1 & -1 & 3 &5 \\&0 & 0 & 0 & 1 &5\\&6 & \frac{3}{2} & -\frac{3}{2} & 3 & 0 \end{bmatrix}$$   a) Find the nullspace of A (Nul(A) = span\{…\}).   b) Find a basis for the column space of A.   c) Is A invertible? Justify your answer using 3 different reasons using the Invertible Matrix Theorem.  

Glass is a brittle material.