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identify the nonlinear terms. (i) 2x – y +z – t = sin- 2 (ii) x ++z+w = 4

identify the nonlinear terms. (i) 2x – y +z – t = sin- 2 (ii) x ++z+w = 4

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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1. (a) Determine which one of the following equations are linear equation. If nonlinear identify the nonlinear terms. 2x – y+ z - t = sin- x +2+z + w = 4 (i) (ii) y (b) Solve the system of linear equations using Gauss-Jordan elimination technique 2x + y + 2z + 3t = 13 -x + 2y + 4z – t = -5 3x + 2y – 6z +t = 4 4x – 3y + 2z – 2t = 6 Write the general solution in vector form. Find the cubic polynomial function p(x) = a + bx + cx² + dx³ such that p(1) = 1, p'(1) = 5, p(-1) = 3, and p'(-1) = 1. 2. 3. (a) If A be an n xn invertible matrix. Prove that the inverse of A is unique. (b) Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, [1 A = |2 3 Lo -2] 1 -1] Hence compute (3A)-1. 4. (a) Use row reduction to evaluate the determinant of the matrix, [2 3 -1 4 3 B = 1 -1 1 1 2 [2 1 -3 3] 1. 1 (b) Determine the values of x so that the matrix A = |1 x is invertible. Lx 5. (a) Find two vectors of norm 1 that are orthogonal to the vectors u = -2 v = (b) If u = (1,3, –2) and v = (2,–1,4). Find the distance between the vectors d(u, v) and d(v,u).
Transcribed Image Text:1. (a) Determine which one of the following equations are linear equation. If nonlinear identify the nonlinear terms. 2x – y+ z - t = sin- x +2+z + w = 4 (i) (ii) y (b) Solve the system of linear equations using Gauss-Jordan elimination technique 2x + y + 2z + 3t = 13 -x + 2y + 4z – t = -5 3x + 2y – 6z +t = 4 4x – 3y + 2z – 2t = 6 Write the general solution in vector form. Find the cubic polynomial function p(x) = a + bx + cx² + dx³ such that p(1) = 1, p'(1) = 5, p(-1) = 3, and p'(-1) = 1. 2. 3. (a) If A be an n xn invertible matrix. Prove that the inverse of A is unique. (b) Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, [1 A = |2 3 Lo -2] 1 -1] Hence compute (3A)-1. 4. (a) Use row reduction to evaluate the determinant of the matrix, [2 3 -1 4 3 B = 1 -1 1 1 2 [2 1 -3 3] 1. 1 (b) Determine the values of x so that the matrix A = |1 x is invertible. Lx 5. (a) Find two vectors of norm 1 that are orthogonal to the vectors u = -2 v = (b) If u = (1,3, –2) and v = (2,–1,4). Find the distance between the vectors d(u, v) and d(v,u).
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