Use the graphing calculator to solve if possibleA=begin{bmatrix}1 & 0&5 1 & -5&70&3&-4 end{bmatrix}B=begin{bmatrix}3 & -5&3 2&3&14&1&-3end{bmatrix}C=begin{bmatrix}5 & 2&3 2& -1&0 end{bmatrix}D=begin{bmatrix}5 -34 end{bmatrix}Find the value in row 2 column 3 of AB-3B

Find a basis for the space of $2\times 2$ diagonal matrices.
$\text{Basis }=\{\left[\begin{array}{cc}& \\ & \end{array}\right],\left[\begin{array}{cc}& \\ & \end{array}\right]\}$

Let B be a 4x4 matrix to which we apply the following operations:
1. double column 1,
2. halve row 3,
3. add row 3 to row 1,
4. interchange columns 1 and 4,
5. subtract row 2 from each of the other rows,
6. replace column 4 by column 3,
7. delete column 1 (column dimension is reduced by 1).
(a) Write the result as a product of eight matrices.
(b) Write it again as a product of ABC (same B) of three matrices.

Find a basis for the eigenspace corresponding to each listed eigenvalue of A below.
$$A=\left[\begin{array}{cc}1& 0\\ -1& 2\end{array}\right],\lambda =2,1$$

How close to 0 do we need to take x so that
$(x^2+6x+9)<9.001?$

Prove that the eigenvalues of a Hermitian matrix are real.

Use the definition of continuity and the properties of limits to show that the function is continuous on the given interval.
${\displaystyle g\left(x\right)=2\sqrt{3}-x,(-\mathrm{\infty },3]}$

$\left[\begin{array}{ccc}0& 2& 4\\ 4& 4& 1\end{array}\right]-\left[\begin{array}{ccc}2& 3& 3\\ -2& 4& -2\end{array}\right]$