Q1: Show that A × Adj(A) = Adj(A) × A = det(A) XI -10 3 Q2: Given A = 1 3 4, compute the inverse using formula 1. 3 1-2 Q 3: Given three points, (7, 8, 9), (8, 10, z), and (2, 4, 6), find the z- coordinate of the second point such that they will be laid in the same plane. 17 10 101 Q 4: Is the matrix M = 4 3 5 singular? 3 2 Q5: Compute the expression det(35)+det(Min33(S)) + 2tr(S)+det(S¹) [1-1 5 where, S = 3 2 lo 2 3.

Q: Are the following two sets of coefficients orthogonal? -1, 0, 0, 1 -1, 1, 0, 0 Yes No

A: Given data is as follows: -1,0,0,1 -1,1,0,0 Yes the following sets of coefficients are orthogonal as…

Q: Use Cramer's rule to solve the following equations I-y+:=1 2r +:= 2 3r+y-3: 3

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Q: Solve for x, where u = (1, -1, 2), v = (0, 4, 1), and w: %3D 5u – 2x = 3v + w X =

A: It is vector problem.

Q: For what values of z and y is orthogonal to both (-1 and

A: Remark: We know that two vectors are orthogonal if they are perpendicular to each other. i.e., the…

Q: N 3 -1l Find the adjoint of A: A =| 1 6 3.Then verify that A (adj A)= (det A)I. 2 -4 0

A: Verification:Compute adj(A) as follows.

Q: Given u = 4i - 7j and v=-6i+ 9j, what is u - v?

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Q: If z = 1+ 2i and w = 3+ 4i, express the following in the rectangular form: (a) 2|w| +(1 – i)2² w + z…

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Q: Q1: if AB = i + 4j – 2k and B is the point (5,1,3), find point A.

A: Note: -Since you have asked multiple questions, we will solve the first question for you. If you…

Q: Let u = PQ and v = PR ; where P = (2, – 1, 3) Q = (0,5, 1) and R = (5,5,0) find a. The component…

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Q: b. Solve the following equations using Cramer's Rule 4x + 2y = 10 Зх— 5у %3D 1

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Q: Perform the vector addition: (– 7, 1) + ( – 12, 3)

A: Given,          <-7,1>+<-12+3>

Q: Use the adjoint of A to find A−1, where

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Q: for z=1+5i and w=3+i, find z/w Write the result a+bi

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Q: Let ā = 7i – 3 and 6 = 3ỉ – 73. Find ā - b

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Q: Find the inverse of ƒ(x) = -x + b (b constant). What angle does the line y = -x + b make with the…

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Q: -3 . Let vi = V2 = 2 V3 -6 and p = 6. 3 3 14 . -69 Determine if p is in Col A, where A = [v, v2 V3].

A: • Col A is the column space of matrix A which is the set of all possible linear combinations of the…

Q: Find the value of ‘v’ in v2 – 2v -15 = 0, if v is a natural number.

A: Given quadratic equation is,

Q: Find the point P such that v = PQ has the components (-7.75, –8.25, – 16). О 3D (-2.75, -2.25, -6) P…

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Q: Let Z₁ Z1 If = 22 m= n = F/1, and Z₂ = -3-4i, -40 +-=-5 i, calculate m and n: n

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Q: Let x = (-2,7,-7) and y = (1,6, 6) be in R°. Compute the following: x + y = ( -5x x – y = ( -5 x +…

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Q: A= 1-1-1 Anda diagonal D and an orthogonal mats P to which PT AP-D. The mas D should have to…

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Q: 3. Find all real numbers t for V = (20 t,4t - 4,5t², t²) are orthogonal. - which = (1,5t,-4t, t³)…

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Q: Given u⃗ =⟨2,−5⟩ and v⃗ =⟨4,−4⟩, find the dot product u⃗

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Q: Given u = - i+j, v = 2i-6j, and w= -2j, find proju (v +w). proj (v + w) = (Type your answer in terms…

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