(8) (Section 5.1 # 5) In this problem you are W is a subspace of V and explain why V R3 given a vector V and a subset W. Decide whether or not R3 a1, a2 E R} {(1,a1,a2)) W

Q: Find the rank of the following matrices.

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Q: (Section 5.3) i. Show that the vectors v₁ = (1, 2, 3, 4), №₂ = (0, 1, 0, −1), and v3 = (1,3,3,3)…

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Q: Find the distance of the point (1, 7, -9) in R from the subspace of vectors of the form (a, 8a, b).

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Q: Find the dimension of the subspace spanned by the given vectors

A: The rank of a matrix is the number of nonzero rows in the reduced matrix.

Q: Section 4.5 - The Dimension of a Vector Space Prereqs: Basis (4.3), coordinate vector and coordinate…

A: The given vectors are .The aim is to prove the given vectors are basis.

Q: Please go through each option with explanation

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Q: The vector x is in a subspace H with a basis B = {b₁,b₂}. Find the B-coordinate vector of x. - 2 4H9…

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Q: 1 2 0 0 3 1 -1 2. Express 14 as a linear combination of the columns of A = Then 2 0 0 1 find a…

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Q: 1 2 . Let uj = |0 u2 = 4 and u3 = 1 1 1 -2 (a) Show that {u1,u2, U3} is an orthogonal set.

A: "Since you have asked multiple question, we will solve the first question for you. If you ant any…

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Q: (7) Given the following pieces information, describe the set of solutions x such that Ax = b: (a) b…

A: We shall solve first question only as you have asked more than one unrelated questions • for others…

Q: Find the rank f the Mathisx by Normal form 3 5 1. 3 13 2. 2 8.

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Q: 5.6. Are the polynomials 1-2x+3x², 2+x-x², 1-2x+x² linearly independent in the vector space P₂? If…

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Q: Section 1.5:  Exercises : 2(b,d,f) only!

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Q: Linear algebra

A: Consider the set

Q: Question 1) The dimension of the subspace of P3 consisting of all vectors of the form at³ +bt² + ct…

A: (1) Given: at3+bt2+ct+d, b=2a-5d, c=d+4a ∴abcd=a2a-5d4a+dd            =a1240+d0-511 Therefore the…

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Q: Section B: Determine of the following set W is subspace of V=R³: W-{(a, 1, 1): a ER).

A: We have to determine whether the set W is a subspace of V=R3.…

Q: linear algebra

A: To prove the linear independence of the three given vectors.

Q: a2 E R³ are subspaces of R³? (No justification necessary.) Which of the following sets of vectors аз…

A: Vector subspace : A subset W of a vector space V  over the scalar field K is a subspace of V if and…

Q: -6 -0-0-0-8 9 6 Let v₁ = -3 4 3 = 1. Is w in {V1, V2, V3}? Type "yes" or "no". 13 9 and w= 6 10 4.…

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Q: Determine if the given set W is a subspace of the given vector space V. If so, find a possible basis…

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Q: Let S = {(1,0, 1), (0, 1,0)} be two vectors in R³. Write the following vectors as a linear…

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Q: If a vector is in the range of a matrix A, then it is also in the null space of A. true of false?

A: Answer

Q: If the set {(1, 2, 1), (0, 1, 1), (1,–1, A)} is linearly independent, then (A) A# -2 (B) A # 2 (C) A…

A: The objective is to find the correct option.

Q: Which of the following vectors are linearly independent? I know that you can use row operation to…

A: To determine if a set of vectors is linearly independent, use the following techniques:1. Zero…