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)

Q: (b) x1 + x2 + 2x3 = 5 + x3 = -2 2x1 + x2 + 3x3 = 3 %3D X1 %3D %3D

A: We see from the given system that, if we add first two equations, we will get the third equation.…

Q: 1. Consider the following system of linear equations: T1 + kr2 = 2 kri + x2 + 13 =1 X1+ x2 + x3 =k…

A: Here the given matrices are                                      A=abcd and B=dcba We have to show…

Q: Express the following system of linear equations as a vector equation. 1x1 +4x2 - 6x3 = -5 -2x1 +…

A:

Q: et V₁ = (1, -2,-2), V₂ = (0, -1, -2), V3 = (2, -4,-5). re the vectors 1, 2 and 3 linearly…

A:

Q: Write a system of equations that is equivalent to the given vector equation. 2 -3 + X3 X1 - 3 + X2 2…

A: We will find which option is correct as following.

Q: 35. For m = (-5, -6) and = (6, −9) find the sum of the vector three times the magnitude of m and the…

A:

Q: The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors V₁, V₂, and v₂…

A: Linear Combination:       A vector V is called a linear combination of vectors   v1, v2, . . ., vn…

Q: Calculate the area of the parallelogram determined by the points (-1 , -1), (2 , 4), (4 , 3) and (7…

A:

Q: X₁ A. 2 -4 O C. 7 -5 HHH + X3 1 Choose the correct answer below. + X₂ 2x₁ + 7x₂ + 5xX3 = 0 4x₁ + 5x₂…

A:

Q: The vectors 3 -4 3 = 12 w = -8 5 -23 + k 7 are linearly independent if and only if k +

A: Solution:-

Q: Determine whether u= (-1, 11) is a linear combination of x =(1,3) and y=(2,-1).

A:

Q: Let a₁ = , a₂ = [2] and b = -7° -13 -8 s b a linear combination of a₁ and a₂? OA. b is not a linear…

A:

Q: Suppose the solution set of a certain system of linear equations can be described as x₁ = 5+ 3x3, x₂…

A: Given,The solution set of a certain system of linear equations can be described as with  free. Aim:…

Q: 2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 =…

A:

Q: Let W= W= , V1 = , V2 = V3 = If possible, express w as a linear combination of the vectors v₁1, V2…

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.