Compute the product AB by the definition of the product of​ matrices, where Ab_1 text{ and } Ab_2 are computed​ separately, and by the​ row-column rule for computing AB. A=begin{bmatrix}-1 & 2 2 & 55&-3 end{bmatrix} , B=begin{bmatrix}4 & -1 -2 & 4 end{bmatrix} Determine the product AB AB=?

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

Using Matrices, solve the following: A practical Humber student invested 20,000 in two stocks. The two stocks yielded 7% and 11% simple interest in the first year. The total interest received was $1,880. How much does the student invested in each stock?

Find three $2\times 2$ idempotent matrices. (Recall that a square matrix A is idempotent when $A^2=A$)

Write the given expression without the absolute value symbol. |x − y| − |y − x|

Show the concept of addition of matrices Along with an example.

Solve the system of given equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.
$\{\begin{array}{l}3a-b-4c=3\\ 2a-b+2c=-8\\ a+2b-3c=9\end{array}$