Texas Instruments TI-89 User Manual - Page 863

real(list1) ⇒ list Returns the real parts of all elements. real(matrix1) ⇒ matrix Returns the real parts of all elements. real({a+iù b,3,i}) ¸ {a 3 0} real([a+iù b,3;c,i]) ¸ [ac 30] 4Rect MATH/Matrix/Vector ops menu vector 4Rect Displays vector in rectangular form [x, y, z]. The vector must be of dimension 2 or 3 and can be a row or a column. Note: 4Rect is a display-format instruction, not a conversion function. You can use it only at the end of an entry line, and it does not update ans. Note: See also 4Polar. [3,pà4,pà6]4Rect ¸ [3ø4‡2 3ø ‡2 4 3ø2‡3] [a,b,c] ¸ [aø cos(b)ø sin(c) aø sin(b)ø sin(c) aø cos(c)] complexValue 4Rect Displays complexValue in rectangular form a+bi. The complexValue can have any complex form. However, an reiq entry causes an error in Degree angle mode. Note: You must use parentheses for an (rq) polar entry. In Radian angle mode: 4e^(p/3)4Rect ¸ (4p/3)4Rect ¸ In Gradian angle mode: (1100)4Rect ¸ p 4øe 3 2+2ø 3øi i In Degree angle mode: (460)4Rect ¸ 2+2ø 3øi Note: To type 4Rect from the keyboard, press 2  for the 4 operator. To type , press 2 '. ref( ) MATH/Matrix menu ref(matrix1[, tol]) ⇒ matrix Returns the row echelon form of matrix1. 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(matrix1)) ù rowNorm(matrix1) Note: See also rref(). ref([ë2,ë2,0,ë6;1,ë1,9,ë9;ë5, 2,4,ë4]) ¸ 10 ë 2/5 1 ë 4/5 4/7 4/5 11/7   0 0 1 ë 62/71 [ ] [a,b,c;e,f,g]!m1 ¸ a b c e f g ref(m1) ¸ 1 f e g e   0 1 aøgì cøe aøfì bøe Appendix A: Functions and Instructions 863