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row number n................................. column number • • • • • Example 1 Assign 10 to the cell at row 1, column 2 of the following matrix : r 1 2 Matrix A : 3 4 L 5 6 Old EDS (ED (MAT) CD (Mat) 110+Mat IÂLPHÂ1 Ix^tI (A) IshiftI f+1 ( T ) IT| |~?~| |~2~| !B( ] )W • • • • • Example 2 Multiply the value in the cell at row 2, column 2 of the above matrix by 5 s (El (MAT) E (Mat) I Mat fi[2,2]x5 11S(A)(s1t)Œ)([)(I][I](I] !B( ] )*f w 20010101 2-8-14 Matrix Calculations • To fill a matrix with identical values and to combine two matrices into a single matrix [OPTN]-[MAT]-[Fill]/[Augmnt] Use the Fill command to fill all the cells of an existing matrix with an identical value and the Augment command to combine two existing matrices into a single matrix. • • • • • Example 1 To fill all of the cells of Matrix A with the value 3 K 2 (MAT) h (Fill) dQ 2(MAT)b(Mat)aV(A)W 2 (MAT) b (Mat) av (A) w • • • • • Example 2 To combine the following two matrices : 3 A = 2] b-[3] K 2 (MAT) f (Augmnt) 2 (MAT) b (Mat) aV (A) Q 2 (MAT) b (Mat) ai(B)W # The two matrices you combine must have the same number of rows. An error occurs if you try to combine two matrices that have different numbers of rows. 20010101 2-8-15 Matrix Calculations • To assign the contents of a matrix column to a list [OPTN]-[MAT]-[M^List] Use the following format with the Mat^List command to specify a column and a list. Mat ^ List (Mat X, m) ^ List n X = matrix name (A through Z, or Ans) m = column number n = list number • • • • • Example To assign the contents of column 2 of the following matrix to list 1 : 1 2 Matrix A 3 4 L 5 6 K 2 (MAT) i (M^List) 2 (MAT) b (Mat) av (A) HO a K1 (LIST) b (List)b W K 1 (LIST) b (List) b w H # You can also use !! b (List) in place of K1 (LIST) b (List). # You can use Matrix Answer Memory to assign the results of the above matrix input and edit operations to a matrix variable. To do so, use the following syntax. • Fill (n, Mat a) ^ Mat f • Augment (Mat a, Mat f) ^ Mat y In the above, a, f, and y are any variable names A through Z, and n is any value. The above does not affect the contents of Matrix Answer Memory. 20010101 2-8-16 Matrix Calculations ■ Matrix Calculations [optn]-[mat] Use the matrix command menu to perform matrix calculation operations. • To display the matrix commands 1. From the Main Menu, enter the RUN • MAT Mode. 2. Press |K to display the option menu. 3. Press 2 (MAT) to display the matrix command menu. The following describes only the matrix commands that are used for matrix arithmetic operations. • {Mat} ... {Mat command (matrix specification)} • {Det} ... {Det command (determinant command)} • {Trn} ... {Trn command (transpose matrix command)} • {Ident} ... {Identity command (identity matrix input)} All of the following examples assume that matrix data is already stored in memory. 20010101 2-8-17 Matrix Calculations > Matrix Arithmetic Operations [OPTN]-[MAT]-[Mat] • • • • • Example 1 To add the following two matrices (Matrix A + Matrix B) : A = r1 H B = 2 3 _1 _ 2 1 J L 2 1 J A B 2 (MAT) b (Mat) av (A) ffl 2 (MAT) b (Mat) ai(B)W • • • • • Example 2 Calculate the product to the following matrix using a multiplier value of 5 : Matrix A 1 2 L 3 4 ] A f B 2 (MAT) b (Mat) BV(A)W ..... Example 3 To multiply the two matrices in Example 1 (Matrix A x Matrix B) A B 2 (MAT) b (Mat) av (A) * 2 (MAT) b (Mat) ai(B)W ..... Example 4 To multiply Matrix A (from Example 1) by a 2 x 2 identity matrix A B 2 (MAT) b (Mat) av (A) * 2 (MAT) g (Ident) C W T Number of rows and columns # The two matrices must have the same dimensions in order to be added or subtracted. An error occurs if you try to add or subtract matrices of different dimensions. # For multiplication (Matrix 1 x Matrix 2), the number of columns in Matrix 1 must match the number of rows in Matrix 2. Otherwise, an error occurs. # When performing matrix arithmetic operations, inputting the Identity command at the location of a matrix command (such as Mat A) makes it possible to perform identity matrix calculations. 20011101 2-8-18 Matrix Calculations • Determinant • • • • • Example Obtain the determinant for the following matrix : [OPTN]-[MAT]-[Det] 1 2 3 Matrix A = 4 5 6 _ -1 -2 0 IoptnI [F2l(MAT)|T|(Det)[F2l(MAT)rn(Mat) |Det Mat R av(A)w • Matrix Transposition [OPTN]-[MAT]-[Trn] A matrix is transposed when its rows become columns and its columns become rows. • • • • • Example To transpose the following matrix : Matrix A 1 2 3 4 L 5 6 K 2 (MAT) H (Trn) 2 (MAT) b (Mat) av(A)w # Determinants can be obtained only for square matrices (same number of rows and columns). Trying to obtain a determinant for a matrix that is not square produces an error. # The determinant of a 2 x 2 matrix is calculated as shown below. I Al = aii ai2 a2i a22 ]■ aiia22 - ai2a2i # The determinant of a 3 x 3 matrix is calculated as shown below. I A I = aii...

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