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.

Select the property of a material, which would help in recording application (for example Hard Disk, CD, DVD etc)

In compression test, the strain develops in the loading axis is  

Load divided by original cross-sectional area is called as Elasticity.

A mechanical property, which measures the degree of plastic deformation, is called as ductility

Atom is made up of