Q5) Answer true or false for the followings: i) in triple dot of vectors (A x B). C = (B x A). C, where the vectors A, B, and C are not same plane. ii) in triple cross of vectors (A x B) x C = Cx (B x A). iii) A is 2 x 2 unit matrix, B inverse of matrix A then A = B. iv) in complex number z³. (z)² = |z|².z

Q: If vector A = [4,1] and vector B = [-3,2] and A-B = [-1,-1]  Sketch the computation above and…

A: Given; vector A = [4,1] and vector B = [-3,2]

Q: Q) Let û = 2745, Vz+3 , and w=T-5 find Scalars a and b such that u - av + bw

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Q: i) Using Gaussian Elimination method, verify that x, = 2, x2 = -1, and x3 = 3. ii) Show that b is in…

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Q: Determine if the vectors are Linearly Independent or Linearly Dependent. -2 [1 -5 =|2.X2) = -3 ,x6)…

A: A set of n vectors of length n is linearly independent if the matrix with these vectors as columns…

Q: Do question 12 only

A: The given in item #12 is:∫04π​​∫01​∫0x2​xcos(y) dz dx dy Consider the innermost…

Q: Three vectors (PQ), (PR), (QR) have been written in matrix form as shown below: 2 -17 PQ1 1 PR = -2…

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Q: Which matrix could be used to rotate a vector 64 degrees clockwise about the origin? cos (-64) sin…

A: we have to find  matrix could be used to rotate a vector 64 degrees clockwise about the origin.

Q: Suppose we know that Write A 6 as a linear combination of the vectors 5 8- 5 6 = 0 H + 6 1 1 -DE-B H…

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Q: how that vectors[ A-2i+ 3j - 2k,B=I +2j+ 4k ] are perpendicular to each o

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Q: If a vector is expressed in terms of i and j, explain how to find the scalar multiplication of the…

A: The vector quantity has both magnitudes as well as the direction. if we multiply a vector by a…

Q: ー0 Let A = -3 -8 %3D そ 14 Label the colmn vectors C ,s,C3, and Cy respeutively. let b. be a linear…

A: The given matrix is ;                     A =  577-10-311-86713914 If  C1 , C2 , C3  and  C4  are…

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

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Q: Do question 10 only

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Q: 3) Find the vector projection of A onto B. (Projs A). b\ If possible, use matrix inversion method to…

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Q: Do question 9 only

A: Step 1: Compute the Gradient of 𝑓Given f(x,y)=x2ey,Compute the partial…

Q: Verify the identity Ax(BXC) = B(AC) - C(A-B) using the following vectors A = ax + 2ay + 3az B = ax…

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Q: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

A: we will write the given vector as linear combination of vectors in as and find the unknown…

Q: Let a = (a1, a2), b = (b₁,b2) be vectors in R². The area(a, b) is given by 1b₂-a2b₁. (a.) Show that…

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Q: X1 – 3x2 = 2 2х, + 5х, %3D—1 a) Inverses b) Cramer's Rule

A: using the specified method to solve the given system.

Q: Find the components of the vector - 4c based on the vector shown.

A: The magnitude of the vector in x direction is represented by i component. The magnitude of the…

Q: 5 3 -2 -3 w = -3 |; A= 4 -5 2 2 -5 4 -1 . Determine if vector w is in Nul(A)

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Q: If a, b and c are three non-coplanar vectors, then find the value of a.(bxc) b.(cxa) c.(bxa) +…

A: Use the properties of vector box product as follows: a→.(b→×c→)=[a→ b→ c→]=[b→ c→ a→]=[c→ a→…

Q: 4 16 -- 12 -21 4. Is the vector in the span of the vectors 10 12 -8 and 8 ? Explain!

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Q: O Find a vector perpendicular to both i- 3j+2k and 5i-j-4k

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