1. Multiplying Matrices

2. Scalar Multiplication - each element in a matrix is multiplied by a constant.

3. **Multiply rows times columns.
**You can only multiply if the number of columns in the 1st matrix is equal to the number of rows in the 2nd matrix.
They must match.
Dimensions:
3 x 2
2 x 3
The dimensions of your answer.

4. Examples: 2(3) + -1(5) 2(-9) + -1(7) 2(2) + -1(-6) 3(3) + 4(5)
3(-9) + 4(7)
3(2) + 4(-6)

5. *They don’t match so can’t be multiplied together.*
Dimensions: 2 x x 2
*They don’t match so can’t be multiplied together.*

6. 2 x 2 2 x 2 *Answer should be a 2 x 2 0(4) + (-1)(-2) 0(-3) + (-1)(5)
1(4) + 0(-2)
1(-3) +0(5)

7. Determinants

8. **To find a determinant you must have a SQUARE MATRIX!!**
Determinant - a square array of numbers or variables enclosed between parallel vertical bars.
**To find a determinant you must have a SQUARE MATRIX!!**
Finding a 2 x 2 determinant:

9. Find the determinant:

10. Finding a 3x3 determinant: Diagonal method
Step 1: Rewrite first two columns of the matrix.

11. 126 - (-52) 126 + 52 = 178 Step 2: multiply diagonals going up!
-224
+10
+162
= -52
Step 2: multiply diagonals going up!
Step 3: multiply diagonals going down!
+12
-126
+240
=126
Step 4: Bottom minus top!
126 - (-52)
= 178

12. 38 - 38 = 0 Step 1: multiply diagonals going up!
-18
+50 +6
= 38
Step 1: multiply diagonals going up!
Step 2: multiply diagonals going down!
- 15 45
+ 8
= 38
Step 3: Bottom minus top!
= 0

13. Expansion of a Third-Order Determinant

14. example:
Evaluate using expansion by minors.

16. You try…
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