For problems 4 and 5, refer to the matrices shown below and perform the indicatedoperations, if possible. Calculator use is optional.2.A =-2-1B =01%3D%3D-51-1-214 -6TC =3-1D =1%3D-281L2 -4104. BC5. A+ BDI3.

This is a matrix multiplication and addition problems.

Answered: For problems 4 and 5, refer to the…

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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In each part, find the matrix X solving the given equation. - [39]-[2-28] *- a. X = X = -4 -6 -10 0 -5 * *-* 3 *- [1] b. X = X = 0 1 -8 d. 9 8 - [11] x = [2 3] X C. 0 -1 X = 1 -2 -7 (3)x= [7] X 6 -11 4 -7 X =
13. Solve the following (given as the augmented matrix): -4 1 71 1 | -5 5 1 10 31 -2 3 20
13. Solve the following system of equations by using the inverse of the coefficient matrix: 8.4x - 1.2y = 10.8 3.5x + 2.6y (Round to the nearest tenth) = 6.4 (S 5.2 or W 5.2)
I. GIVEN THE FOLLOWING MATRICES -2 0 -5 A = a. (5A)¹ = 5 (A¹) b. (8A)BA(8B) 5 3 4 II. Find the inverse of a matrix. a. 2-3] -12 b. 3x+2y=6 5x-9 y = 15 C. -1 1 -6 12 34 X = III. SOLVE FOR THE VALUES OF THE VARIABLES SUCH THAT EACH OF THE FOLLOWING STATEMENTS IS TRUE B = a. The sum of three numbers is 12. The 1st is 5 times the 2nd. The sum of the 1st and 3rd is 9. Find the numbers. 7 4 2 b. -5 0 2 3x-2y+z=25 x + 3y - 2z = -12 4x - 5y-z=31 -3 2 -6 1 -1 3 2 12 -2 -2 1 IV. SOLVE THE GIVEN SETS OF LINEAR EQUATIONS BY:0 (a) Cramer's Rule (b) Gaussian elimination method (c) Gauss-Jordan Method a)
For the following system of equations: X1 + 3x2 + x3 = -10 4x1 – 2x2 + 2x3 = -16 2x1 + x3 = -9 А. Find the PLU factorization of the coefficients matrix. Verify that PA = LU where L is a strict lower triangle matrix. Solve the system using the PLU factorization you found in part (a). В. С.
A certain drug is made from only two ingredients: compound A and compound B. There are 3 milliliters of compound A used for every 4 milliliters of compound B. If a chemist wants to make 567 milliliters of the drug, how many milliliters of compound A are needed?
A small software corporation borrowed $292,500 to expand its software line. Some of the money was borrowed at 9%, some at 10%, and some at 12%. Use a system of equations to determine how much was borrowed at each rate if the annual interest was $29,900 and the amount borrowed at 10% was 22 times the amount borrowed at 9%. Solve the system using matrices. Step 1 Let the amount borrowed at 9% be x, the amount borrowed at 10% be y, and the amount borrowed at 12% be z. The total amount borrowed was $292,500. The total annual interest was $29,900. The amount borrowed at 10% was 2- times the amount borrowed at 9%. Write a set of equations using the information given. Convert the percentage to decimal fraction. x + y + z = 292,500 .09 x +.10 y + |.12 V z = 29,900 X x - y = 0 Write the associated augmented matrix for the given system of equations. Recall that since there are three equations in the system, the matrix will have three rows. Use the coefficients of x, y and z as entries of the…
Q.2 Solve the following set of equations using the inverse of the coefficient matrix: 8x2+2xy=-7 2xy +5x2-8-3x1 6x₁+2x2-26-8xy

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For problems 4 and 5, refer to the matrices shown below and perform the indicated operations, if possible. Calculator use is optional. 4 = 2 -2 3 5. B = %3D -5 1 -1 0 -2 4 -6 3. 7 -1 C = 1 -2 2 -4 D = 3 1 10 4. ВС 5. A+ BD