14.2 Homework Problems: Matrices
1. Add or subtract the following matrices
a. [latex]\left[\begin{matrix}3&-6&2\\7&7&6\\\end{matrix}\right]-\left[\begin{matrix}2&1&-3\\4&5&5\\\end{matrix}\right][/latex]
b. [latex]\left[\begin{matrix}-2&0\\5&7\\5&4\\\end{matrix}\ \right]+\left[\begin{matrix}-2&3\\7&7\\-7&6\\\end{matrix}\ \right][/latex]
2. If A = [latex]\left[\begin{matrix}-5&5&-4\\-2&2&2\\\end{matrix}\right][/latex] and [latex]B=\ \left[\begin{matrix}-3&-6\\2&3\\6&1\\\end{matrix}\right]\ \ \ find\ AB[/latex]
3. If A = [latex]\left[\begin{matrix}4x&xy\\\end{matrix}\right][/latex] and B = [latex]\left[\begin{matrix}x^2&0&6xy\\-6x&0&-3\\\end{matrix}\right][/latex] find AB
4. If A = [latex]\left[\begin{matrix}3&1&6x\\-4y&0&-1\\\end{matrix}\right][/latex] find (3 · A)
5. Put the following systems of equations into matrices but do not solve
a. 5x + 2y – 2z = -1
2x – z = 7
-4x + y = -21
b. 10m – 4u + 8w = -2
6m = 5u – 4w + 6
17u – 4 = w
6. Solve the systems of equations using the Matrix Method
a. x + 2y = 3
2x – y = -4
b. 7x + 2y = 24
8x + 2y = 30
c. -2x + 4y + z = -3
x – 3y + 2z = 11
x – 2y + 3z = 12
d. x – y + 5z = -6
x + 2z = 0
6x + y + 3z = 0
e. 3x + 4y = 11
x + y = -2
2y + z = -4