u = (2, 3,-1) v= (0, 1, -2) w = (2, 4, -3).

Q: Find the vector z, given that u = ⟨1, 2, 3⟩, v = ⟨2, 2, −1⟩, and w = ⟨4, 0, −4⟩     (1/3)z − 3u = w

A:

Q: 2. Choose the linearly dependent vectors in R

A: two non zero vectors V1, V2 are said to be linearly independent if and only if aV1+bV2= 0 ⇒ a=0 and…

Q: Find the two unit vectors orthogonal to both a = (3, 1, 1) andb = (−1, 2, 1).

A: Given: a=3,1,1 and b=-1,2,1

Q: Are the following sets of vectors linearly independent? Show the details of your work. [3 4 0 1], [2…

A:

Q: Let v, w, and a be nonzero vectors such that v · a = w · a.Is it true that v = w? Either prove this…

A: Given: v, w and a is non zero vectors, such that: v·a=w·a To prove: v=w

Q: Why are there no vectors u and v in R,, such that ||u.||= 2, ||v|| = 3, and    uxv= -7?

A: The given values are, u=2, v=3,   and  u×v=-7. The objective is to find the valid reason for the…

Q: Given the vectors ū = (-2, 1, 1) and V = (3, –1, 1), calculate the vector projection of ū onto V

A:

Q: 2. Show that if the vectors v,, v2, .,Vm are mutually orthogonal then they are linearly ...…

A:

Q: Verify the Pythagorean Theorem for the vectors u and v.u = (1, −1), v = (1, 1)

A:

Q: Are the following vectors linearly independent? Yes No , ,,

A:

Q: (d) Suppose the three vectors x, y, z E R³ are known to be linearly independent. Are the three…

A:

Q: Let y = 2-| = H and u = Write y as the sum of two orthogonal vectors, ₁ in Span {u} and 2 orthogonal…

A:

Q: Show that there are no vectors u and v such that 11u 11= 1, ||v|| = 2, and uxv= 3.

A: If u and v are two vectors, and the angle between these two vectors is θ Then the magnitude of the…

Q: Without doing any calculations, explain why the following sets of vectors are linearly dependent:…

A: Since you have posted multiple question with multi part we are supposed to give solution of first…

Q: Which of the following vectors is coplanar to [1, 1, 1] and 2, 3]?

A:

Q: Let v = 2i - 5j and w = i - j.Decompose v into two vectors, v1 and v2, where v1 is parallel to w and…

A: v=2i-5j  and  w=i-j. Now, v·w=2i-5j·i-j=21+-5-1=2+5=7 & w=12+-12=2

Q: Determine all vectors v that are orthogonal to u.u = (0, −4, 3)

A: Given u=(0,-4, 3)we have to find all vectors v that are orthogonal to u,If u.v =0 then vectors u and…

Q: Determine if the given vectors are coplanar u = 2i - j - k; v = 4i + 3j + 2k; w = 6i + 7j + 5k

A:

Q: Find all vectors in R* that are orthogonal to both 1 1 V1 = and V2 2 -2

A: Linear Algebra: The vectors are: v1=112-2v2=2112Let denote the vector v3=v1v2v3v4

Q: Determine if the vector v is a linear combination of the remaining vectors.

A: Given vectors are: v=123; u1=110; u2=011 If the vector v is a linear combination of the remaining…

Q: Find the weighted Euclidean inner product (u, v) = -3v1 u1 – 3vzuz of the given vectors. u = (u, v)…

A: Given u, v=-3v1u1-3v2u2 u=-3-2, v=14

Q: Show that the vectors 1 – t,1+ 2t² , t² +t+1, t² + 2tare linearly dependent and indicate how one of…

A: Given Vectors:V1 = 1-tV2 = 1+2t2V3 = t2+t+1V4 = t2+2tgiven vectors are linearly dependent, then…

Q: Find the value of t such that the vectors v=(2t+1,-3,3t-2) and w=(7,4t+2,2) are orthogonal.

A:

Q: Are the following vectors Linearly Independent? Show your work vų = [2 4 – 5], v2 = [7 2 – 1],v3 =…

A: Let x, y , z be three scalers. Condition for these vectors to be independent :

Q: Prove that if vector u is orthogonal to both vectors v and w, then u is orthogonal to v + w.

A:

Q: Determine whether the following vectors are linearly independent in R2:

A:

Q: 7 Consider the vectors: U = 1 v = w = -2 2 Express W as a linear combination au + bv. What is b'?

A: WRITE  W AS A LINEAR COMBINATION OF U AND V ie. w = au + bv Using Row Elementary Transformation,

Q: Are the following sets of vectors linearly independent? Show the details of your work. 17. [3 4 0…

A: We have   Solve using row-echelon form

Q: Prove that the vectors v= and w= are orthogonal.

A:

Q: Determine all vectors v that are orthogonal to u.u = (11, 2)

A: Now let

Q: Determine whether the vectors u= i + 5j − 2k,  v = 3i − j and w = 5i + 9j − 4k are coplanar

A: We have to determine whether the vectors u= i + 5j − 2k,  v = 3i − j and w = 5i + 9j − 4k are…

Q: If the vectors b, c, d are not coplanar, then can we say that the vector (ā×b)×(ē×d) + (ā×ē) × (dxb)…

A:

Q: Let v = 2i - 5j and w = i - j. Decompose v into two vectors, v1 and v2, where v1 is parallel to w…

A: Given vectors are: v = 2i - 5j and w = i - j The formula for the vector projection is given by…

Q: Find the coordinate vector of w relative to the basis S = { u1, u2} for R u 1 = (4, – 4), u 2 = (4,…

A: Given: u1=4,-4u2=4,4w=0,24

Q: Determine all vectors v that are orthogonal to u.u = (0, 5)

A:

Q: If u • vx w or v • or w • v equal to zero, then the vectors u, v , and w are coplanar... True False

A: Concept Used: Three vectors are said to coplanar if their scalar triple product is zero That is  [u→…

Q: Let u, v and w be vectors in Cn . Clearly prove that (u + v) · w = u · w + v · w.

A:

Q: If X and Y are linearly independent vectors in R", then {0,X,Y} is linearly independent.

A:

Q: Find x if the vectors a =i+j+ 2k;b = xi-j+k; coplanar or linearly dependent.

A: Given,       a=i+j+2kb=xi-j+kc=3i-2j-k

Q: Find all vectors in R2 that are orthogonal to u = (2,1).

A:

Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = ( – 1,…

A: find the explanation below

Q: Find the vector z, given that u = ⟨1, 2, 3⟩, v = ⟨2, 2, −1⟩, and w = ⟨4, 0, −4⟩.      z = u − v + w

A: Given:                                                          u = <1, 2,…

Q: Show that if u and v are linearly independent vectors, then so are  u + v and u -v.

A: Given :           u and v are linearly independent vectors.   To prove :               u + v and…

Q: IH A and B are any two vectors in V, prove that (A- B) x (A + B) = 2(A X B).

A:

Q: Show that the following vectors of v,(R) are LI : a, = (1, 1, 0); a, = (1, 1, 1); a, = (2, 1,3)

A: Introduction :

Q: Let u and v = .A vector orthogonal to both ú and v is

A:

Q: Find a vector that is orthogonal to both u and v, given u = 2i + 3j + 2k and v = 3i +j + 2k 5i + 4j…

A:

Q: Write y as the sum of two orthogonal vectors, x1 in Span{u} and x2 orthogonal to u

A:

Q: Prove that in R², the vectors {v1, v2, V3} are always dependent. What about if we have two vectors…

A: