Given the ordered basis B = {p1 = 9 + 2æ, p2 = -4 – x}, find [p]B, the coordinates of p = -39 – 9x with respect to B. %3D Ex: 5 [P]B %3D

Q: Given u = (4, -2) and v = 3i + 5j. Find u + v, v - 2u, and -6u + 5v in component form.

A: ai + bj + ci + dj = (a+c)i+ ( b+d)j

Q: Find the conjugate of z = -2 – 4i, and compute zz. z = zz =

A: Given that: z=-2-4i

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

A:

Q: Find a + b, 2a + 3b, lal, and la - bl. a = i +3j - 4k, b = -3i -j + 6k a+b= 2a + 3b = |a| = |a - b|…

A: Given vectors  a = i + 3j - 4kb = -3i - j + 6k

Q: Find the real component of In(z + 2w) if

A:

Q: Find a b. . a = 8i + j, b = i-4j+ k

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Q: Find the real numbers x and y if (x – iy) (3 + 5i) is the conjugate of –6 – 24i.

A:

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: Find z,(-1,2) if z=In(5x°y²+2y*). Answer:

A: We can find the answer as below.

Q: Determine values of x and y so that v · w = 0 and v · u =

A: There are vector representation given as, v=x1y , w=x-20  and u=0-9y. To find the value of  x  and y…

Q: Let a = - 5i + 33 + 2k and b = - 4i – 3 + 4k. Find a x b. ä xb = k

A: Cross product is the binary operation on two vectors in three dimensional space. It again results in…

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: Express (-2/3+ j2) in rectangular form.

A: Rectangular form of the given complex number

Q: Z= 2 + 5j Y= -3 - 3j D= -2 + 6j Find the conjugate of the numbers above

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

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Q: Let a = 4i + 3j – k, b = 2i – j + xk and c = yi + zj – 2k. Find: %3D %3D a x such that a and b are…

A: Two vectors are said to be perpendicular to each other if their dot product is zero. We will use…

Q: Given ü = (2,-3) and = (-2,5) find ü v %3D

A: Solution is done in step 2

Q: Compute the order of each element in the Quaternions, Q8. Show your work.

A:

Q: Express −i+j in the form [a,b]

A: Simplification

Q: Given that v = (2,3, 4), vị = (1,0,1), v2 = (0,-1, 1), vz = (-1,-1,1). Express v as a linear…

A: Given, v=2,3,4, v1=1,0,1, v2=0,-1,1, v3=-1,-1,1

Q: Find the cross product (-2i – j+ k) × (–3i – j – k).

A:

Q: Which of the following is the dot product of u = 4i + 6j – 5k and v =-10i – 8j + 10k? -3 60 -138

A: To find the dot product of the given vectors u=4i+6j-5k  &  v=-10i-8j+10k. Note that:…