Question 15: Do the vectors below form a basis for R3? If so, explain. If not,...
Please answer all if possible. Question 15: Do the vectors below form a basis for R3? If so, explain. If not remove as many vectors as you need to form a basis and show that the resulting set of vectors form a basis for R3. C1 = -- () -- () -- () -- (1) Question 16: Carefully consider if equalities below valid for matrices. For each equality state if there is a restriction on dimensions under which they are...
tion 135 The matrix A = b c df 9 Lh j k] has a determinant of 6. 3d 29 -6f (a) What is the determinant of the matrix B = 3a 2c - 6b 3h 2k-6j] List the row & column'operations that were performed on A to produce B and state what each of these operations' does to the determinant 3d 39 3f (b) What is the determinant of the matrix C = 2a 2c 25 -6h -6 Explain...
Notes Ask Your Te 0/2 points The given vectors form a basis for R3. Apply the Gram-Schmidt Process to obtain an orthogonal basis. Then normalize this basis to obtain an orthonormal basis. (Enter sqrt(n) for vn.) -4 sqrt(3)2sqrt(30) 32/15sqt 4 1 Need Help? TltoTuter
5. The given vectors form a basis for a subspace W of R3 or R4. Apply the Gram- Schmidt Process to obtain an orthogonal basis for W 2 1 W1 = W2 = 3 -1 0 4. 1 , W3 = 1 2 1
5. The given vectors form a basis for a subspace W of R3 or R4. Apply the Gram- Schmidt Process to obtain an orthogonal basis for W 2 3 1 W1 = W2 W3
5. (a) (7 marks) Determine whether the following sets form a basis for R3. Explain your answers. i. - {0:0} - {0:00) - {000) -*-**(0-1 1 (b) (3 marks) Is the set W = a vector space? Explain your answer.
(4) 2. Which of the sets of vectors in 1-(a) through 1(d) form a basis for R3? Explain why. Hint Use your answers in question (1).
thank you very much Exercise 4.10.52 Consider the vectors of the form :11, v, w ER〉 2w-2v-811 Is this set of vectors a subspace of R3? If so, explain why, give a basis for the subspace and find its dimension.
Question (7) Consider the vector space R3 with the regular addition, and scalar aL multiplication. Is The set of all vectors of the form b, subspace of R3 Question (9) a) Let S- {2-x + 3x2, x + x, 1-2x2} be a subset of P2, Is s is abasis for P2? 2 1 3 0 uestion (6) Let A=12 1 a) Compute the determinant of the matrix A via reduction to triangular form. (perform elementary row operations) Question (7) Consider...
For which real values of x do the following vectors form a linearly dependent set in R3?v1= (x, -1/9, -1/9)v2= (-1/9, x, -1/9) v3= (-1/9, -1/9, x)