1. Essential Question: Why, oh why, didn’t I take the blue pill?

2. 4-2: Adding and Subtracting Matrices  A matrix equation is an equation where the variables represent matrices. You solve them like regular equations. [ 11 32 ] X – [ 01 89 ] = [ 11 32 ] + [ 11 32 ] + X [ 12 11 ] =

3. 4-2: Adding & Subtracting Matrices  Your Turn: Solve for X [ 0 25 ] X + [ 107 -44 ] = [ 0 25 ] – [ 0 25 ] – X [ 117 -6 ] =

4. 4-3: Matrix Multiplication  Matrices can be multiplied (or divided) by a real number. The real number factor (such as 3) is called a scalar. Simply distribute the number outside to all numbers inside. [ 35 28 ] 3 [ 915 624 ] =

5. 4-3: Multiplying Matrices  Putting it all together. [ 68 -42 ] 4X + [ 100 42 ] = [ 68 -42 ] – [ 68 2 ] – 4X [ 4-8 80 ] = [ 34 -21 ] 4X + 2 [ 100 42 ] =  4 X [ 1-2 20 ] =

6. 4-3: Multiplying Matrices  Your Turn. Solve for X. [ ] – [ ] – -3X [ 309 -21-156 ] = [ 70 2-34 ] -3X + [ ] =  -3 X [ 0-3 75-2 ] = 1008 -19-1810 70 2-34 70 2-34

7. 4-2: Adding & Subtracting Matrices  Equal matrices are matrices that, not only have the same dimensions, but all their corresponding elements match Determine whether the two matrices are equal: [ -23 50 ] [ -8 / 4 6 – 3 15 / 3 4 – 4 ] = [ 49 85 ] [ 8/28/2 10 / 2 16 / 2 18 / 2 ] = Yes, same dimensions and all elements match No, the terms on the right side don’t match

8. 4-2: Adding & Subtracting Matrices  Remember, for matrices to be equal, both their dimensions and all elements must match. Solve for x and y [ 2x – 54 33y + 12 ] [ 254 3y + 18 ] = 2x – 5 = 25 + 5 + 5 2x = 30  2 x = 15 3y + 12 = y + 18 – 12 – 12 3y = y + 6 – y –y 2y = 6  2 y = 3

9. 4-2: Adding & Subtracting Matrices  Your Turn Solve for x and y [ 3x4 ] = [ -9x + y ] x = -3 4 = x + y 4 = -3 + y 7 = y

10. 4-2 & 4-3  Assignment Page 178, 10 – 17 (all problems) Page 186, 1 – 9 (odd problems)