One of the following is always true A) If det(A) = det(B), then det(A+ B) = 2det(A) B) adj(AB) = adj(A)adj(B) %3D C) B = adj(A), then AB = I D) If A is invertible, then (adj(A))- = zatA) det(.

Q: Let A be 4x4 and det(A)=3. Then det(24)=. and det (A" A)=.

A: Given A be a 4×4 matrix and detA=3

Q: Find A and B such that 2x-1/(x+1)(3x+2) = A/x+1 + B/3x+2

A:

Q: Evaluate the commutators of the operators (a) d/dx and 1/x, (b)d/dx and x2.

A: Given:  a)  ddx and 1x b) ddxand x2 To Find: Commutator of the operators

Q: Let a = (1,2, 3), b = (1,0, –1) and c = (2, 1, 3). (a) Verify that a · (2 b+c) =2(a · b) + (a · c).

A: a=(1,2,3) , b=(1,0,-1) and c=(2,1,3)

Q: If A- A = I, then (4-1) = %3D

A:

Q: If A and B are orthogonal, is A+B also orthogonal?  Can you demonstrate Algebraically using A + B =…

A: Solution: Given-   A and B are Orthogonal matricesTo show:  (A+B)  is OrthogonalSince, A and B are…

Q: (d) Develop an estimated regression equation for the data of the form ý = b, + b,x + b,x. (Round b,…

A: e) Consider the following table for necessary calculations. y x x2 12 22 484 22…

Q: Let 1 2 A = 3 6 Is A invertible? Explain your answer.

A: To verify is the given matrix A is invertible Or not.

Q: Prove Boolean Equation:  XY+X(Y+Z)+Y(Y+Z) = Y+XZ

A: We shall solve this problem using the TRUTH TABLE as shown below.The truth table for the Left-hand…

Q: (2) Write v as a lincar combination of u₁, U₂, U3 if possible, where U₁ = (2,3,5), u₂ = (1, 2, 4),…

A: Given that,  V=(10, 1,4)  u1=(2, 3,5), u2=(1, 2,4) , u3=(-2, 2,3)  To find : a, b, c such that…

Q: Prove c (A + B) = cA + cB   (c + d)A = cA + dA   c(dA) = (cd)A  IA= A

A:

Q: Suppose I + AB is invertible. Show that I + BA is also invertible by showing that (I + BA)¯ = I –…

A: Assume that I+AB is invertible.  Then, I+ABI+AB-1=I ⋯ 1. Use equation (1) and calculate…

Q: Two fair six-sided dice are rolled (one maize and one blue), with outcomes X and Y respectively for…

A: Since the outcome of one die doesn't depend upon the outcome of the other die. The value rolled for…

Q: verify that det(A B) = det(B A) and determine whether the equality det(A + B) = det(A) + det(B)…

A:

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

A:

Q: Let V3 = {(a, b)|a, b E R} with the following operations: (a₁, a₂) + (b₁,b₂) = (a₁ + b₁, a₂ + b₂)…

A:

Q: Q4\Use Cramer's Rule to find the values of x, y, and z from the following equations: 2x + 3y - z = 1…

A:

Q: Find A and B are independent, positively associated or negatively associated, in each of the…

A: ANSWER: From the given data,

Q: A - (B U C) = %3D (А - B) U (A — С) (A – B) U C Option 1 Option 4 (А- В - С) (A – B) n (A – C)

A: given , A-(B∪C)  WE HAVE TO FIND EQUIVELENT TO IT FROM GIVEN FOUR OPTION

Q: Show that (AB)T and BTAT are equal.

A: Now,

Q: +(x-1)+(x-1)+qy-2)+ Expanding Equation (3) and simplifying, we obtain the following equation…

A: Equation (3):We have to prove equation (4) which is:Formula used:here, , and .Therefore,

Q: Compute u + v, 2u – v, 3u – 2v, and 0 – 3v if (a) u =| 2 3 2 (b) u= = -3 (c) u = 1 4

A: (a) Consider the given matrices, u=123 and v=201 now, use the matrices addition property,…

Q: Prove that (A = B) where (A = ax + ay + az) and (B = bx + by + bz)?

A: Given- A=ax+ay+az and B=bx+by+bz To Prove- That A=B

Q: Letflx): 3x-2:9 x)=5x+1 Compute the indicated Values, a, lfogl (3) blfef) (oJ d, (gog) (-7) )e.…

A:

Q: If both z + w and zw are real, how to prove that either z = w (conjugate) or Im(z) = Im(w) = 0?

A:

Q: = kA modulo m for the given values of k, A, and m.

A:

Q: Find a number z (except 0) such that Az³ + Bz²+ Cz = D 2 1 3 0 -2 -4 00 ^-[ ] ³-R2 :]-[+]-[1] B= 1 2…

A: Solution

Q: The value of a' for which f : R → R, ax +7 flx) is invertible lies in %3D 2 x* +4 (а) (0, 2) (b) (1,…

A:

Q: 7. (FE) Let A = a b C de f and B = 2a 26 a+d b+e 9 h 2c c+f i (a.) By using permutation approach,…

A:

Q: If 8 = (AB)–- (AB), then with usual notation, prove that %3D (i) [(A)- (a)] [(B)- (B)] + 2 N 8 (AB}…

A: ANSWER: For the given data,