Matrices are arrays of numbers arranged in rows and columns. The order of a matrix specifies the number of rows and columns. Entries are the individual numbers within the matrix. Basic matrix operations include addition, subtraction, scalar multiplication, transpose, and multiplication. Matrix multiplication is only defined when the number of columns of the first matrix equals the number of rows of the second matrix. The determinant provides a scalar value for a square matrix and is used to determine properties like invertibility. Excel can be used to perform matrix operations through functions like MMULT and control-shift-enter.

1. Matrix and Determinant Operations

3. A matrix is any doubly subscripted array of elements arranged in rows and columns.

4. What is the order? 3 x 3 3 x 5 2 x 2 4 x 1 1 x 4 (or square matrix) (Also called a row matrix) (or square matrix) (Also called a column matrix)

5. Row Vector [1 x n] matrix

6. Column Vector [m x 1] matrix

7. Identity Matrix Square matrix with ones on the diagonal and zeros elsewhere.

8. Transpose Matrix Rows become columns and columns become rows

10. = = 7 7 4 5 0 7 5 7

12. = 5-2 -4-1 3-8 8-3 0-(-1) -7-1 1-(-4) 2-0 0-7 = 2 -5 -5 5 1 -8 5 3 -7

14. -2 6 -3 3 -2(-3) -5 -2(6) -2(-5) -2(3) 6 -6 -12 10

15. Matrix Multiplication Matrices A and B have these dimensions: [r x c] and [s x d]

16. Matrix Multiplication Matrices A and B can be multiplied if: [r x c ] and [ s x d] c = s

17. Matrix Multiplication The resulting matrix will have the dimensions: [ r x c] and [s x d ] r x d

18. Multiplying Two Matrices

20. Determinants of a three by three cross matrix

21. Matrix Operations in Excel Select the cells in which the answer will appear

23. Matrix Multiplication in Excel Enter these three key strokes at the same time: control shift enter

24. Multiplying Two Matrices using Excel

25. Thank you