Given the vectors a = (3, 2, 1, 5) and b = (-2,3, 1,0). (a) Find the vector component of a orthogonal to b. (b) Find a homogeneous linear system of two equations in four unknowns whose solution space consists of those vectors in R' that are orthogonal to a and b. (c) Find the vector equation for the solution space of the system in (b). (d) What kind of geometric object is the solution space for the system in (b)?

Given the vectors a = (3, 2, 1, 5) and b = (-2,3, 1,0). (a) Find the vector component of a orthogonal to b. (b) Find a homogeneous linear system of two equations in four unknowns whose solution space consists of those vectors in R' that are orthogonal to a and b. (c) Find the vector equation for the solution space of the system in (b). (d) What kind of geometric object is the solution space for the system in (b)?

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter1: Systems Of Linear Equations

Section1.1: Introduction To Systems Of Linear Equations

Problem 72E: Find a system of two equations in three variables, x1, x2 and x3 that has the solution set given by...

See similar textbooks

Similar questions

Find a system of two equations in three variables, x1, x2 and x3 that has the solution set given by the parametric representation x1=t, x2=s and x3=3+st, where s and t are any real numbers. Then show that the solutions to the system can also be written as x1=3+st,x2=s and x3=t.
find a homogeneous linear system of two equations in three unknowns whose equation in three unknowns whose solution space consists of those vectors in R^3 tha are orthogonal to a=(-3,2,-1) and b=(0,-2,-2)
Let x be a solution to the m × n homogeneous linear system of equations Ax = 0. Explain why x is orthogonal to the row vectors of A.
Verify that the given vector X is a solution of the given homogeneous linear system
From the system x' = -x + 5y og y' = -y show that the vector function (top of picture) is a solution of the system only if (bottom of picture) is true.
Derive Cramer’s rule for a system of linear equations Ax = b, where A denotes a 3-by-3 matrix
If A is invertible, i.e., for any given r.h.s. vector b, the system Ax = b has a solution. How can you compute the 3rd column of A^−1(what r.h.s. b would youchoose)?
apply Jacobi's method to the given system.Take the zero vector as the initial approximation and work with four-significant- digit accuracy until two successive iterates agree within 0. 001 in each variable. In each case, compare your answer with the exact solution found using any direct method you like. 4.5a -0.5b = 1 a -3.5b = -1
apply Jacobi's method to the given system.Take the zero vector as the initial approximation and work with four-significant- digit accuracy until two successive iterates agree within 0. 001 in each variable. In each case, compare your answer with the exact solution found using any direct method you like. 3a + b = 1 a+ 4b+ c = 1 b + 3c = 1
Describe the solutions of the given system into parametric vector form. x1+x2+ 2x3= 9 2x1+ 4x2−3x3= 1 3x1+ 3x2+ 6x3= 27 Also compare this solution, geometrically, with the solution set of the following homogeneous system. x1+x2+ 2x3= 0 2x1+ 4x2−3x3= 0 3x1+ 3x2+ 6x3= 0
Vectors contained within the three-dimensional space vector are given. In order to create linear combination of three vectors v1 = mv2 +nv3 , how can we obtain coefficients m and n?
What is the value of each of the constants that are part of the linear combination between the vectors 2i+3j−k, (8, −7, 2) and (1, −1, 1) so that the vector (11 , −29, 11) is the result of that combination?