2 Let A = then det(3AT) - 18 -6 -2 II

Q: ds if s = Find dt 7t + 3 ds dt II

A: We have given;

Q: 23. Given that 4sinh - 2coshx = Ae*+ Be* then A and B are respectively А. 1,-3 C. -1,-3 В. -1,3 D.…

A: Topic- trigonometry

Q: Yk+1Yk – 2yk - -2 into the linear o quation ea

A: Given,                     yk+1yk-2yk=-2                                (6.38)

Q: Evaluate fc 713 where C : |z| = 2. Ans. fc z+1)3 Ti ( – 4). 1 z² (z+1)³

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Q: Compute A?x and A3x the correct way: ´1 0 () 0 1 A = 3 0 2 0 1 1 1

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Q: Let 21 = 2+ j3 and z 4 j5. Evaluate

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Q: 8. Provide justification for you what will appear on the ex asked. (-1)" (2n)! (a) n=1 n4 – 4n -

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Q: 1. If x=27-3k and y = i +5j -4k, express each of the following in terms of i, j, k b) 2(3x+y)-3(4y…

A: Given x→=2i→-3k→ & y→=i→+5j→-4k→To write expression in terms of i→,j→,k→:

Q: Verify that (AB)T = BTAT.

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Q: Let z1 = 2+ j3 and z2 = 4 – j5. Evaluate 1+2 %3D 21-22

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Q: v.(AX 8) - 8 ·/TXA) – A (vX 8) Prove the earuation.

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Q: 3. Show that if A-1 exists, then f eAT dr = A-(eAt – I) = (e4t – I)A-1.

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Q: 3 Let A = -6 -1 -2 and v = -6- -2 3 Av = -6 2 -9 Ex: 5 s v in null(A)? Select an option

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Q: Compute AB, where A AT B = = 24 09 4 -3 -1 and B = 76 (1 %). 6 4

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Q: 6. Evaluate the det A where A = 1 0 -1 2 4 24 3 1 0 1 0 041 44

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Q: -6 -3 0 3. [15p] А: and B Show that det A+det B ± det(A+B). 0 -12 1 9

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Q: If z1 and zą both satisfy z +z = 2 |z - 1| and arg (21– 2): then find Im (21 + z2). 4'

A: let z1 = x1+iy , z2 = x2+iy2

Q: 2 Let C: z-2|=1 and I = dz. Then C z2-4

A:

Q: If (R – {0}, .) = (Q,.) then 1=0 1=-1 -1=0

A: For the given statement

Q: (b) Use the value of det(A) to evaluate 1 2 3 3 -2 3 3 1 1 1 2 -2 -3 -1 4. 1 3 -2 4) 2. 2. 021

A:

Q: Let A= 1 o d - [1 2 11 0 1 0l and B= 1 -1 %3D 3 Then (BAT-2A") is equal to

A:

Q: 27) Calculate AC, BC and (A + B)C. Also, verify that (A + B)C = AC + BC 0 6 71 ΓΟ 1 1] 2 If A = -6 0…

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Q: -10 If AXT = B, then X= Let A = %3D 0 2

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Q: 1. If x=27-3k and y = 7+57-4k, express each of the following in terms of i, j, k a) 5x-2y

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Q: find A1 ∩B1 , GIVEN THAT                                             U= {x ∈ z/ - 7}    A= {x ∈ Z+…

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Q: am+nu 3. axməyn' if u = (x² + y²)e*+y

A: Problem is related to (m+n)th order partial derivative. Here simultaneous differential needs to…

Q: a) If Z1 = -3 + 3i and Z2 = 4i. Show that: i) Arg(Z,Z2) + Arg(Z,) + Arg(Z2) ii) Arg (2) = Arg(Z,) –…

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Q: o In general a;jk(Xi + Yj)Zk = a¡jkX¡Zk + AijkYiZK - True - False

A: We have to prove or disprove that

Q: 3) Compute A-1 using adjoint. -1 -2 -3 -41 1 2 3 Let A = 5 1 0 0

A:

Q: If z̟ = 1 + jb , z2 = re¬j² , z1/z2 = -10, determine all possible values of b and r.

A: According to the given information, it is required to determine the possible values of b and r.

Q: If A is a 2 x 2 with det(A) = 3, then det(4A1) = %3D

A: det(A-1)=1det(A) det(4A-1)=4ndet(A-1) where n is the order of the matrix.

Q: Q2/ prove [A] [A] = [I] if [2 4 -5 [A]= 2 7 1 3 4

A:

Q: Compute A B, where A AB= 0 -2 2 -2 0 2 -4 7 8 -5 -1 2 and B = 8 -2 1 -5 -1 3

A: This question can be solved using the concept of multiplication of matrices.

Q: T: M22 --->M22 defined by T(A) = AB,

A: Given, a matrix B, and defined a map T(A) = AB, where T: M2×2  ---> M2×2. We have to find the…

Q: Consider z1 = 1 - j2 and z2 = -2 + j3. Determine Im (21)?

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Q: Let a-2-3j.kb-41-) and c-1-31-2k. If d is such that da-9. db-7 and dc-6, then d is equal to 01-31-2…

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Q: 1) Find all associates of (i) [6] in Z10, (ii) [4] in Z5.

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Q: If l2 = 3 compute DI, and D = -1 -2 and I2D.

A: Given- I2=1001 and D=23-1-2. To compute- The value of the expression DI2 and I2D.

Q: X Compute A*; Btr BA,(BA tr BA, (BA)O [ - 5 -4 I B -a 3 -3 5

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Q: Let C: z-il-3 and I = 6. edz $ dz. Then z2 O I- 1= 4ni

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Q: 21 Let vi = 4 V2 = -7,V3 3 6 Does (V1, V2, V3) Sspan R?

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Q: a) Expand Ca-b)Catb) b) Hence, expand ox-y+2)(ctytz)

A: a) Expanding (a - b )(a + b)  (a - b)(a + b) =  a(a+b) - b( a+b)                        =  a.a + a.b…

Q: Write equation for each ellipse

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Q: 0 1] -1 3 -2 0 0 1 Compute det (B), where B 3 det (B*)

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Q: 27 1 2-r2 4. Evaluate: r dz dr de Jo

A: Solution

Q: 4. Find the dual of the following LP: max z = - 4x1 - X2 4x + 3x2 6 X1 + 2x2 s 3 3x1 + x2 = 3 s.t.…

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Q: 1 2 1 -Given that B= 1 -1 0 3 1 1 Show that B,-B,- 6B = 1. Hence, deduce that B' = B² -- B – 61.

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Q: 2. Determine the products C = AB and D = BA if %3D %3D 4 61 -7 A = 1 -5 -1 3 -5 2 %3D -9 --13 -4 7 6…

A: The given matrices are A=46−7−51−9−3114×2 and B=−13−52−13−4762×4.

Q: (16) Show that AB=BA for 1 5 0 0 A = 0 3 0 0 0 and B = 3 1 2

A: