what is the dimension of the vector space formed by the solution of the system of the following equation? 2X+2Y+2Z=0 2X- 2Y+OZ=0 2X=2Y=2Z=0 O 1 02 O 3 O o
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- 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.Explain the steps for solving a system of equations using Cramer’s rule.Find a system of two equations in two variables, x1 and x2, that has the solution set given by the parametric representation x1=t and x2=3t4, where t is any real number. Then show that the solutions to the system can also be written as x1=43+t3 and x2=t.
- -3 x₁ + x₂ + 3x3 = 0 - 6x₁ + 3x₂ + 3x3 = 0 2x₁3x₂ + 5x3 = 0 Write the solution set of the given homogeneous system of equations in parametric vector form. Show all your work, do not skip steps.Find the vector equation of a line that passes through the two points A(3,9,2) and B(−7,1, −4)Suppose the row echelon form of a system of equations is x−2y−9z == −10 y+2z == −1 Enter the components of x,y,z using t for the free variable z - ?,?,? (Enter the components of the vector ⟨x,y,z⟩⟨x,y,z⟩, using tt for the free variable)
- Find a general set of solution vectors x₂ = - 5x2 X₂ = x₁ + 3x₂h> A Moving to the next question prevents changes to this answer. Question 1 +2x2 -X3 +X4 = 3 -2x1 -3x2 +X3 -X4 = 2 X1 Write the solution to the system of equations in parametric vector form. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).Describe the solutions of the first system of equations below in parametric vector form. Provide a geometric comparison with the solution set of the second system of equations below. Зx, + 3x, + 6x3 3 12 - 6х, - 6х2 - 12х3- 24 3x, + 3x, + 6x3 = 0 - 6x, - 6x2 - 12x3 = 0 - 3x, + 3x3 = 0 - 3x, + 3x3 = 12 X1 Describe the solution set, x= X2 of the first system of equations in parametric vector form. Select the correct choice below and fill in the answer box(es) within X3 your choice. (Type an integer or fraction for each matrix element.) O A. X= O B. X= X2 O C. x= + Xa O D. X=X2 + X3
- The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors v,, v2, and v, because 0 = Ov, + Ov, + Ov3. This is called the trivial solution. Can you find a nontrivial way of writing 0 as a linear combination of the three vectors? (Enter your answer in terms of v,, v, and v. If not possible, enter IMPOSSIBLE.) v = (1, 0, 1), v2 = (-1, 1, 2), v3 = (0, 9, 2) 0 = Need Help? Read ItThe zero vector 0= (0, 0, 0) can be written as a linear combination of the vectors v, Va, and v, because 0= Ov, + Ov, + Ov. This is called the trivial solution. Can you find a nontrivial way of writing 0 as a linear combination of the three vectors? (Enter your answer in terms of v, v and vy. If not possible, enter IMPOSSIBLE.) V- (1, 0, 1), v2 = (-1, 1, 2), V3 = (0, 1, 8)The zero vector 0 = (0,0,0) can be written as a linear combination of the vectors v1, v2, and v3 because 0= 0v1+0v2+0v3. This is called the trivial solution can you find a nontrivial way of writing as a linear combination of the three factors?(enter your answer in terms of v1, v2, v3. if not possible, enter impossible)