X = { Ø₁ A₁ A², 3 and X₂ = { 0, B, B², √ ² are o fields but X, U X₂ is not. Why?

Q: -18 -11 -10 E adj A = 2 14 - 4 then absolute value of determinant 4 5 -8

A: In this question, the concept of the determinant is applied. Determinant Determinants are a type of…

Q: 2. Let L1 bg 3D (-1,2, 1,3, 3), сі %3D (3, —4, 0, — 4, 3), сэ %3D Find a basis of Lin L2 and L1+ L2.…

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Q: 2. Find the determinant and invers a) -3 7 9 1 3 4 b) 1 9 3.

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Q: |1 2 3 0 1 1 1 (g) 0 0 1 3 100 2

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Q: 6. Find UV (dot a) Ū · V = (2, 3, -

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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: 9. 4 -6 -21 7 3. 8 -3 4 -7 8 8 0 13 17 31 7 9 4 23 4. -6 11 0 3 6 0

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Q: If A²=0, prove that A cannot be invertible.

A: Given,If A²=0, prove that A cannot be invertible.

Q: Зх — Зу — 6z %3D —3 2х — 2у — 4z %3D 10 2х + Зу + z %3D7 -

A: Given system of equations, 3 x-3 y-6 z=-32 x-2 y-4 z=102 x+3 y+z=7 The objective is to solve the…

Q: 5- Solve the following determinants :- -1 -21 [2 3 1] 2 a) 4 5 31 L1 2 b)-1 2 1 3 -3] [1 d) 0 2 -2…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: 2. Show that (a) Re(iz) - Im z; = (b) Im(iz) = Rez.

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Q: Every combination of v = ( 1 , -2, 1 ) and w = ( 0, 1 , -1 has components that add  to __ . Find c…

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Q: 5. Show that b, is always positive, by establishing the equation (Qn-1,Qn-1) (Qn-2,Qn-2) b,

A: We will apply the properties of inner-product to prove the given statement.

Q: Let A = (1,2), B = (1,3,4) C (2,3, 4} and U = (1,2,3,4,5), then [Cn (B- A)] = O {3.4} O {1.2} O {3}…

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Q: Suppose S and T are nilpotent operators which conmmutes i . e., ST TS. Show that S + T and ST are…

A: Provided that S and T are two nilpotent operatorswhich are conmmuting with each others That is ,…

Q: 2. Prove that if AB = AC, then B need not equal C unless A is invertible.

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Q: EXER 7: MATRICES Prove that if N is invertible then MN¹ = N¹M if and only if MN=NM.

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Q: all your calculations and simplify your answer completely. Il you only give a final an- Swer you…

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Q: Find x, y, z and w if (::)-(; )-(.. ") 4 x + y 3 -1 2w z + w 3

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Q: Suppose S and T are nilpotent operators  which conmmutes i.e., ST=TS.  Show that S+T and ST are also…

A: Provided that S and T are two nilpotent operatorswhich are conmmuting with each others  That is ,…

Q: If x,y,z are real numbers satisfying the equation 25 (9x* +y° )+9z²-15(5xy+yz+ 3zx )=0 then prove…

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Q: B- Find the determinate ^ = 1 B 1 Lo 2 3 -2 C -2

A: For the 2*2 matrix we can find determinants by multiplying the diagonal numbers and find the…

Q: 10.

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Q: [10 0 A = |4 1 0 1 0 1 2 4 0 1 3 0 1 Determine whether or not A is invertible. (Justify your answer)

A: A is invertible

Q: 9) /(x) = 3 · -8 -6 -4 -2 | x + 1 20 18 14 1 12 10 8 ଣ 4 + 2 2 4 6 X

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Q: Verify that (AB)T = BTAT.

A: Now,

Q: 6. Show that there is a one-to-one correspondence between the Cartesian products A x B x C and A x…

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Q: 1. Lat A - [; : - and B = 2 2 1 3 4 (a) Compute AB. (b) Compute BA.

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Q: 1 a 0 b 1 -1) 31 For which values of a and b is-2 invertible? Why?

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Q: 7. Evaluate the determinate |1 2 (d) 2 5 2 5 7 1 5 8 (e) 1 7 9 5 5 12 3 2 1 (f) 2 3 4 1 4 1

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Q: Uz + xuy = x²y, u (x, 2x + = 5x 2 %3D

A: Lagrange method for solving partial differential equation: Let us consider differential equation:…