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

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

4-2: Adding & Subtracting Matrices  Your Turn: Solve for X [ 0 25 ] X + [ ] = [ 0 25 ] – [ 0 25 ] – X [ ] =

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. [ ] 3 [ ] =

4-3: Multiplying Matrices  Putting it all together. [ ] 4X + [ ] = [ ] – [ 68 2 ] – 4X [ ] = [ ] 4X + 2 [ ] =  4 X [ ] =

4-3: Multiplying Matrices  Your Turn. Solve for X. [ ] – [ ] – -3X [ ] = [ ] -3X + [ ] =  -3 X [ ] =

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: [ ] [ -8 / 4 6 – 3 15 / 3 4 – 4 ] = [ ] [ 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

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 = x = 30  2 x = 15 3y + 12 = y + 18 – 12 – 12 3y = y + 6 – y –y 2y = 6  2 y = 3

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

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