Texas Instruments TI89TITANIUM User Manual - Page 876

simult( ) MATH/Matrix menu simult(coeffMatrix, constVector[, tol]) ⇒ matrix Returns a column vector that contains the solutions to a system of linear equations. coeffMatrix must be a square matrix that contains the coefficients of the equations. constVector must have the same number of rows (same dimension) as coeffMatrix and contain the constants. Optionally, any matrix element is treated as zero if its absolute value is less than tol. This tolerance is used only if the matrix has floating-point entries and does not contain any symbolic variables that have not been assigned a value. Otherwise, tol is ignored. • If you use ¥ ¸ or set the mode to Exact/Approx=APPROXIMATE, computations are done using floating-point arithmetic. • If tol is omitted or not used, the default tolerance is calculated as: 5Eë 14 ù max(dim(coeffMatrix)) ù rowNorm(coeffMatrix) simult(coeffMatrix, constMatrix[, tol]) ⇒ matrix Solves multiple systems of linear equations, where each system has the same equation coefficients but different constants. Each column in constMatrix must contain the constants for a system of equations. Each column in the resulting matrix contains the solution for the corresponding system. Solve for x and y: x + 2y = 1 3x + 4y = ë 1 simult([1,2;3,4],[1;ë1]) ¸ [ë23] The solution is x=ë 3 and y=2. Solve: ax + by = 1 cx + dy = 2 [a,b;c,d]!matx1 ¸ [ac bd] simult(matx1,[1;2]) ¸ ëaø(2døìbbìødc)    2ø aì c   aø dì bø c  Solve: x + 2y = 1 3x + 4y = ë 1 simult([1,2;3,4],[1,2;ë1,ë3]) ¸ [ë2 3 9ë/27] For the first system, x=ë 3 and y=2. For the second system, x=ë 7 and y=9/2. sin( ) 2 W key sin(expression1) ⇒ expression sin(list1) ⇒ list sin(expression1) returns the sine of the argument as an expression. sin(list1) returns a list of the sines of all elements in list1. In Degree angle mode: sin((p/4)ô ) ¸ sin(45) ¸ Note: The argument is interpreted as a degree, gradian or radian angle, according to the current angle mode. You can use ó ,G o r ô to override the angle mode setting temporarily. sin({0,60,90}) ¸ In Gradian angle mode: sin(50) ¸ ‡2 2 ‡2 2 {0 ‡3 2 1} ‡2 2 In Radian angle mode: sin(p/4) ¸ ‡2 2 sin(45¡) ¸ ‡2 2 876 Appendix A: Functions and Instructions