Find a basis for the subspace of R3R3 consisting of all vectors [x1 x2 x3] such...
Find a basis for the subspace of R3R3 consisting of all vectors
[x1
x2
x3]
such that 8x1+5x2−2x3=08x1+5x2−2x3=0.
Hint: Notice that this single equation counts as a system of linear equations; find and describe the solutions.
Homework Answers
Answer = the solution is given below
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Find a basis for the subspace of R3R3 consisting of all
vectors
[x1
x2
x3]
such...
X1 (1 point) Find a basis for the subspace of R3 consisting of all vectors |...
X1 (1 point) Find a basis for the subspace of R3 consisting of all vectors | x2 | such that-3x1 + 5x2 +6x-0. Hint: Notice that this single equation counts as a system of linear equations; find and describe the solutions. Answer
Determine whether the system is consistent 1) x1 + x2 + x3 = 7 X1 -...
Determine whether the system is consistent 1) x1 + x2 + x3 = 7 X1 - X2 + 2x3 = 7 5x1 + x2 + x3 = 11 A) No B) Yes Determine whether the matrix is in echelon form, reduced echelon form, or neither. [ 1 2 5 -7] 2) 0 1 -4 9 100 1 2 A) Reduced echelon form B) Echelon form C) Neither [1 0 -3 -51 300 1-3 4 0 0 0 0 LOO 0...
Solving Systems of Linear Equations Using Linear Transformations In problems 1-5 find a basis for the...
Solving Systems of Linear Equations Using Linear Transformations In problems 1-5 find a basis for the solution set of the homogeneous linear systems. 2. X1 + x2 + x3 = 0 X1 – X2 – X3 = 0 3. x1 + 3x2 + x3 + x4 = 0 2xı – 2x2 + x3 + 2x4 = 0 x1 – 5x2 + x4 = 0 X1 + 2x2 – 2x3 + x4 = 0 X1 – 2x2 + 2x3 + x4...
Find a basis for the subspace of R4 consisting of all vectors of the form (a,...
Find a basis for the subspace of R4
consisting of all vectors of the form (a, b,
c, d) where c = a +
4b and d = a − 6b.
Problem #7 : Find a basis for the subspace of R4 consisting of all vectors ofthe form (a, b, c, d) where c a + 4b and d=a-6b
; Let at be a linear transformation as follows : T{x1,x2,x3,x4,x5} = {{x1-x3+2x2x5},{x2-x3+2x5},{x1+x2-2x3+x4+2x5},{2x2-2x3+x4+2x5}] a.) find the...
; Let at be a linear transformation as follows : T{x1,x2,x3,x4,x5} = {{x1-x3+2x2x5},{x2-x3+2x5},{x1+x2-2x3+x4+2x5},{2x2-2x3+x4+2x5}] a.) find the standard matrix representation A of T b.) find the basis of Col(A) c.) find a basis of Null(A) d.) is T 1-1? Is T onto?
Find all solutions to the system using the Gauss-Jordan elimination algorithm. X1 + 2x2 + 2x3...
Find all solutions to the system using the Gauss-Jordan elimination algorithm. X1 + 2x2 + 2x3 = 12 4x3 24 442 + 12x3 = 24 + 4x2 + 8x1 4x1 + Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The system has a unique solution. The solution is x1 = X2 = X3 = X2 = X3 = S. - <s<00. OB. The system has an infinite number of...
(1 point) Let Find a basis of the subspace of R4 consisting of all vectors perpendicular...
(1 point) Let Find a basis of the subspace of R4 consisting of all vectors perpendicular to ū.
Let x = [X1 X2 X3], and let T:R3 → R3 be the linear transformation defined...
Let x = [X1 X2 X3], and let T:R3 → R3 be the linear transformation defined by x1 + 5x2 – x3 T(x) - X2 x1 + 2x3 Let B be the standard basis for R3 and let B' = {V1, V2, V3}, where 4 4. ---- 4 and v3 -- 4 Find the matrix of T with respect to the basis B, and then use Theorem 8.5.2 to compute the matrix of T with respect to the basis B”....
Problem #7: Find a basis for the subspace of R4 consisting of all vectors of the...
Problem #7: Find a basis for the subspace of R4 consisting of all vectors of the form (a, b, c, d) where c = a + 2b and Problem #7: Select $ Just Save Submit Problem #7 for Grading Problem #7| Attempt #1 Your Answer: Attempt#2 | Attempt#3 Your Mark:
Consider the subspace W C R4 given by X1 X2 W = ER4 X1 + x2...
Consider the subspace W C R4 given by X1 X2 W = ER4 X1 + x2 + x4 = 0 and x2 + x3 + x4 = 0 X3 X4 = Find an orthonormal basis H {h1, h2, h3, h4} for R4 with the property that hy and h2 are elements of an orthonormal basis for W, where orthonormality is defined with respect to the dot product on R4 x R4.
X1 (1 point) Find a basis for the subspace of R3 consisting of all vectors | x2 | such that-3x1 + 5x2 +6x-0. Hint: Notice that this single equation counts as a system of linear equations; find and describe the solutions. Answer
Determine whether the system is consistent 1) x1 + x2 + x3 = 7 X1 - X2 + 2x3 = 7 5x1 + x2 + x3 = 11 A) No B) Yes Determine whether the matrix is in echelon form, reduced echelon form, or neither. [ 1 2 5 -7] 2) 0 1 -4 9 100 1 2 A) Reduced echelon form B) Echelon form C) Neither [1 0 -3 -51 300 1-3 4 0 0 0 0 LOO 0...
Solving Systems of Linear Equations Using Linear Transformations In problems 1-5 find a basis for the solution set of the homogeneous linear systems. 2. X1 + x2 + x3 = 0 X1 – X2 – X3 = 0 3. x1 + 3x2 + x3 + x4 = 0 2xı – 2x2 + x3 + 2x4 = 0 x1 – 5x2 + x4 = 0 X1 + 2x2 – 2x3 + x4 = 0 X1 – 2x2 + 2x3 + x4...
Find a basis for the subspace of R4
consisting of all vectors of the form (a, b,
c, d) where c = a +
4b and d = a − 6b.
Problem #7 : Find a basis for the subspace of R4 consisting of all vectors ofthe form (a, b, c, d) where c a + 4b and d=a-6b
Find all solutions to the system using the Gauss-Jordan elimination algorithm. X1 + 2x2 + 2x3 = 12 4x3 24 442 + 12x3 = 24 + 4x2 + 8x1 4x1 + Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The system has a unique solution. The solution is x1 = X2 = X3 = X2 = X3 = S. - <s<00. OB. The system has an infinite number of...
(1 point) Let Find a basis of the subspace of R4 consisting of all vectors perpendicular to ū.
Let x = [X1 X2 X3], and let T:R3 → R3 be the linear transformation defined by x1 + 5x2 – x3 T(x) - X2 x1 + 2x3 Let B be the standard basis for R3 and let B' = {V1, V2, V3}, where 4 4. ---- 4 and v3 -- 4 Find the matrix of T with respect to the basis B, and then use Theorem 8.5.2 to compute the matrix of T with respect to the basis B”....
Problem #7: Find a basis for the subspace of R4 consisting of all vectors of the form (a, b, c, d) where c = a + 2b and Problem #7: Select $ Just Save Submit Problem #7 for Grading Problem #7| Attempt #1 Your Answer: Attempt#2 | Attempt#3 Your Mark:
Consider the subspace W C R4 given by X1 X2 W = ER4 X1 + x2 + x4 = 0 and x2 + x3 + x4 = 0 X3 X4 = Find an orthonormal basis H {h1, h2, h3, h4} for R4 with the property that hy and h2 are elements of an orthonormal basis for W, where orthonormality is defined with respect to the dot product on R4 x R4.
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