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Resumen del manual
E-14 MAT Matrix Calculations MAT Matrix Calculations The procedures in this section describe how to create matrices with up to three rows and three columns, and how to add, subtract, multiply, transpose and invert matrices, and how to obtain the scalar product, determinant, and absolute value of a matrix. Use the F key to enter the MAT Mode when you want to perform matrix calculations. MAT ..................................................... F F F 2 Note that you must create one or more matrices before you can perform matrix calculations. •You can have up to three matrices, named A, B, and C, in memory at one time. • The results of matrix calculations are stored automatically into MatAns memory. You can use the matrix in MatAns memory in subsequent matrix calculations. • Matrix calculations can use up to two levels of the matrix stack. Squaring a matrix, cubing a matrix, or inverting a matrix uses one stack level. See “Stacks” in the separate “User’s Guide” for more information. k Creating a Matrix To create a matrix, press A j 1(Dim), specify a matrix name (A, B, or C), and then specify the dimensions (number of rows and number of columns) of the matrix. Next, follow the prompts that appear to input values that make up the elements of the matrix. Mat A 23 2 rows and 3 columns You can use the cursor keys to move about the matrix in order to view or edit its elements. To exit the matrix screen, press t. E-15 k Editing the Elements of a Matrix Press A j 2(Edit) and then specify the name (A, B, or C) of the matrix you want to edit to display a screen for editing the elements of the matrix. k Matrix Addition, Subtraction, and Multiplication Use the procedures described below to add, subtract, and multiply matrices. 12 • Example: To multiply Matrix A = 4 0 by [ ] [ ] –2 5 ([ ]) 3–8 5 –1 0 3 Matrix B = –4 0 12 2–4 1 12 –20 –1 (Matrix A 32) A j 1(Dim) 1(A) 3 = 2 = (Element input) 1 = 2 = 4 = 0 = D 2 = 5 = t (Matrix B 23) A j 1(Dim) 2(B) 2 = 3 = (Element input) D 1 = 0 = 3 = 2 = D 4 = 1 = t (MatAMatB) A j 3(Mat) 1(A) A j 3(Mat) 2(B) = •An error occurs if you try to add, subtract matrices whose dimensions are different from each other, or multiply a matrix whose number of columns is different from that of the matrix by which you are multiplying it. k Calculating the Scalar Product of a Matrix Use the procedure shown below to obtain the scalar product (fixed multiple) of a matrix. 2–1 6–3 • Example: Multiply Matrix C = by 3. [ –5 3] ([ –15 9]) E-16 (Matrix C 22) A j 1 (Dim) 3(C) 2 = 2 = (Element input) 2 = D 1 = D 5 = 3 = t (3MatC) 3 -A j 3(Mat) 3(C) = k Obtaining the Determinant of a Matrix You can use the procedure below to determine the determinant of a square matrix. • Example: To obtain the determinant of 2–1 6 Matrix A =5 0 1 (Result: 73) [ ] 3 24 (Matrix A 33) A j 1(Dim) 1(A) 3 = 3 = (Element input) 2 = D 1 = 6 = 5 = 0 = 1 = 3 = 2 = 4 = t (DetMatA) A j r 1(Det) A j 3(Mat) 1(A) = • The above procedure results in an error if a non-square matrix is specified. k Transposing a Matrix Use the procedure described below when you want to transpose a matrix. 57 4 • Example: To transpose Matrix B = [ 89 3 ] 58 7 9 4 3 ([ ]) (Matrix B 23) A j 1(Dim) 2(B) 2 = 3 = (Element input) 5 = 7 = 4 = 8 = 9 = 3 = t (TrnMatB) A j r 2(Trn) A j 3(Mat) 2(B) = E-17 k Inverting a Matrix You can use the procedure below to invert a square matrix. –3 6 –11 • Example: To invert Matrix C = 3–4 6 4–8 13 [ ] –0.4 1 –0.8 –1.5 0.5 –1.5 –0.8 0 –0.6 ([ ]) (Matrix C 33) A j 1(Dim) 3(C) 3 = 3 = (Element input) D 3 = 6 = D 11 = 3 = D 4 = 6 = 4 = D 8 = 13 = t (MatC–1) A j 3(Mat) 3(C) a = • The above procedure results in an error if a non-square matrix or a matrix for which there is no inverse (determinant = 0) is specified. k Determining the Absolute Value of a Matrix You can use the procedure described below to determine the absolute value of a matrix. • Example: To determine the absolute value of the matrix produced by the inversion in the previous example. 0.4 1 0.8 1.5 0.5 1.5 ([ ]) 0.8 0 0.6 (AbsMatAns) A A A j 3(Mat) 4(Ans) = VCTVector Calculations The procedures in this section describe how to create a vector with a dimension up to three, and how to add, subtract, and multiply vectors, and how to obtain the scalar product, inner product, outer product, and absolute value of a vector. You can have up to three vectors in memory at one time. E-18 Use the F key to enter the VCT Mode when you want to perform vector calculations. VCT ..................................................... F F F 3 Note that you must create one or more vector before you can perform vector calculations. •You can have up to three vectors, named A, B, and C, in memory at one time. •The results of vector calculations are stored automatically into VctAns memory. You can use the matrix in VctAns memory in subsequent vector calculations. k Creating a Vector To create a vector, press A z 1 (Dim), specify a vector name (A, B, or C), and then specify the dimensions of the vector. Ne...
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