Answered: For the system shown, 2x-y+3z…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Use the inverse of 1 -4 -7 -1 -1 2 -1 5 X₁ + 2x₂x3 = -3 = 3 (X₁₁ X₂ X3) = -4x₁7x₂ + 7x3 -X₁ - X2 + 5x3 = -2 to find the solutions to the linear system below.
Write the following linear systems in augmented matrix form, wherethe variables are ordered using the regular alphabetical order. 7 − B + 4C − 3D = A + 2 − 3B − 5C5B + 9 = −1 + 2A + 6B + 6C + 2D
6. Solve the system by inverting the coefficient matrix: x₁ + 3x₂ + x3 = 4 2x₁ + 2x₂ + x3 = -1 2x₁ + 3x₂ + x3 = 3
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i) If X,Y,ZX,Y,Z are finite sets, then |X∩Y∩Zc|=|?1∩Y|−|X∩Y∩Z| where ?1=_______ (ii) If X,Y,Z are finite sets, then |X∩Yc∩Zc|=|X|−|X∩?2∩Zc|−|X∩?3∩Z|−|X∩Y∩Z| where ?2=___________ where ?3=___________ (iii) A certain department of mathematics offers three elective courses: a course in abstract algebra (A), a course in mathematical biology (B), and a course in computer science (C). It is known that in a group of 41 students of the department: 29 students took the course in abstract algebra (A), 23 students took the course in mathematical biology (B), and 21 students took the course in computer science (C). 12 students took both (A) and (C), 16 took (A) and (B), 13 took (B) and (C); 8 took all three courses. Write A (resp. B,C) for the set of students who took the course (A) (resp. (B), (C)). (a) Use (i) to find the cardinalities of the fundamental products A∩B∩Cc,A∩Bc∩C,Ac∩B∩C, of the sets…
Consider the system: x+2y+3z=6 2x + 5y +3z=7 x + 8z = 14 a. Write the system as a matrix equation in the form of Ax = b b. Find A-¹ using elementary row operations and the inverse algorithm (show steps completely and carefully. No technology). c. Solve the system Ax = b using your result from part (b) and matrix multiplication. Show the basic steps (though you do not need to show the detail of the matrix multiplication process -- that can be done "in your head"). Your solution should be written as x = (a column matrix, as required for the multiplication)
WHe-the sytems of equations as an augmented "matrix X-34-32= - -5X-3+57=-a (-bX-5y42=-le

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For the system shown, 2x-y+3z = 1 -x-3y+2z = -4 x+2y-2z = 3 Solve by using matrix inversion.