2. Let A = and B = al. Show that det(A + B) = det A + det B if and only if a + d = 0.

Q: If u= (2, 1) and v= (4, –16), find 4u+ v. 4 Select the correct answer below: O (9,0) O (6. –15) О…

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Q: 11 6 linear combinations of x, y, and z, or show that it cannot be done. Let x = 120 and z = TTTT If…

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Q: Let u = (2,6, 4) and 7 = (-1, -2, - 7). Compute the following: ū. v = vu - ||||²

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: Let →u=⟨6,−4,−6⟩ and →v=⟨−5,−3,−6⟩. Compute the following:

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Q: (2 3. Let A = G) and B = (; ). Compute and compare: %3D a. Det(A + B), det(A) + det(B). b. det(3A),3…

A: We have A=2-135 and B=1211 Part(a) Now if we have a matrix M=abcd, then, detM=abcd=ad-bc Therefore,…

Q: Let ā= (2, 5, 7) and 6 = (1, 3, 4). (a - b) × (a + b) = X (3,16,33) X

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Q: 10. Find a and ẞ such that c = αa + ẞb, where a = (-3,0,2), b = (0,-1,2), and c = (-6,5,-10).

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Q: Let an = an-1+ an-2 with ao = 0, a1 = 1. Show that an is even iff ( if and only if) n is a multiple…

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Q: Show that <a, b | a5 = b2 = e, ba = a2b> is isomorphic to Z2.

A: To show that the group <a, b | a^5 = b^2 = e, ba = a^2b> is isomorphic to Z2, we need to…

Q: Show that is isomorphic to Z2.

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Q: 2. (6 marks) Let a, b, c € Z with a 0. Prove that if a X (a + 2b + 3c), then a Xb or a Xc.

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Q: The augmented matrix is given for a system of equations. If the system is consistent, find the…

A: The given augmented matrix is                               14-2-310013-5-1-4-2-919

Q: j+ky-o Find k Iet yco)=lo0 andyc2)=4 3D0

A: Given that y'+ky=0 y(0)=100 and y(2)=4

Q: Suppose v4 = 20 – 02 + 503. Let w = 601 + 202 – 303 – 204. (a) Write w as a linear combination of…

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Q: Let u=(9,−8)​, v=(1,9)​, and w=(−2,7). Carry out the following computation. Find u+v+w.   |u+v+w|=?

A: Given that  Let u=(9,−8)​, v=(1,9)​, and w=(−2,7) To Find u+v+w.

Q: 10.

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Q: Let y = Ա 4 + DIS 5 Ա and u = x³ = x³ - 2x.

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Q: 4. Which relation between x and u yields 16+x² = 4/1+u?

A: Given:

Q: Tpy and B= -1 x² + x² + y² + 1 A<B

A: We have,  and,

Q: Let v = (5, 1, 2) and w = (4, –3, 6). Find each of the following: v+ w, v– 3w, || v||, || v – w ||

A: Solution: The objective is to find the required values