nstead of using the standard definitions of addition and scalar multiplication in R, suppose hese two operations are defined as follows. (a) (x1, Y1, 21) + (x2, Y2, 2) = (xı + x2 + 1, y1 + Y2 + 1, z1 + 22 + 1) c(x, y, z) = (cx + c – 1, cy + c – 1, cz + c – 1) With these new definitions, Show that it satisfies the Axioms 5,6, and 7

Q: conjugate of v-1-3 is 1- V-1+3 2- -V-1-3 -V-1+ 3 3 - V-1 2- 4-

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Q: (4) Use standard multiplication to multiply the two sexigesimal numbers 11, 4; 17, 9 and 50, 50: 43,…

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Q: التاريخ : 2 We can rewrite axt(1-d)y-xo. as follows @q (x-x₂) + (-a)y 2 (x-y)- (X-X₁) a(x-X ₂) +…

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A: Given B has a column of zeros , then to find BA has a column of zero or not .

Q: The real part of csch(1 + j2) is _____.

A:

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A: We have to find the inverse of matrix using Gauss jordan method.

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Q: Describe geometrically (line, plane, or all of R 3) all linear combinations of (a) [ 1/2/3 ] and […

A: We know that a set of vectors u1, u2, ……, un is said to be linearly independent if the equation…

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Q: 1. (10 points) Consider the set V of polynomials of the form ac® + bx4+ca² +d, where a, b, c, d e R.…

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Q: Show that 1 1 1 x2 y? z2 (y² – a²)(z² – a²)(z²? – y²) - - ,4

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Q: Use the adjoint method to compute the inverse of

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Q: 22. Find the zeros off (x) = x³ – 4x² + x + 6

A: we have to find roots

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A: This is a problem of linear transformation.

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A: Given: 4x-7yx-3y+x-2y3y-x For adding given expression, we take L.C.M. and simplify it

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Q: (s² + a²) (s² + b²)

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Q: Find curl (82 i + 9x j + 6y k). curl (82 i + 9x j + 6y k) = = ( )k )i + (i )j + (

A: To Find : curl(8z i + 9x j +6y k)

Q: Let P(R#) represent the set of all polynomial functions, functions that can be written in the form…

A: Given that   P(R#) represent the set of all polynomial functions. Each polynomial in P(R#) can…

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Q: Q.29 Expand the following: (i) (4a– 2b–3c) (ii) | 2p -3 || 2p 1 y+-z (iii)

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Q: -2 Use Gauss-Jordan Method to find the inverse of -4 1. 1

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Q: Q1) Find the inverse of A (1 00 A=2 1 0 5 4 1

A: A=100210541

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Q: Let à = (0, 3, 2), b = (3, 1, 1), and c = (2, 6, 3). a Compute the following: = (a - b) (à · c) :…

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Q: (1) (2) (3) 4 (4) 4(b + a)+(c + a) + Name the property used in (4). 11 = II = 11 distributive…

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Q: y)(Ty → Wy) - Hv)) → Ia

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Q: Which of the following are multiplicative inverses:  (a) 5y/x and 5x/y (b) 5y and 7y (c) 7y/x and…

A: Here we have to find which of the options are multiplicative inverses.

Q: Show that the Newton divided-difference polynomials 3 – 2(x + 1) + 0(x + 1)x + (x + 1)x(x – 1) and…

A: Given: Let P(x)=3-2x+1+0x+1x+x+1xx-1    Q(x)=-1+4x+2-3x+2x+1+x+2x+1x

Q: 2. (a) Define the dot product of two polynomials p(x) = ao+a₁x+a₂x²+a3x³ and q(x) = bo+b₁x+b₂x²+b3x³…

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Q: 4. (4x + )(4x - ) +

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Q: Suppose (x1,x2) + (Y1,Y2) is defined to be (x1 + Y2 ,x2 + Y1). With the usual multiplication cx = (…

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Q: Question 2. Are the polynomials x? – 2x + 1, 2x2 – 3x – 6, a) Linearly independent? -x2 + 5x – 3,…

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Q: D A B D Zax Zo Z₂ Z₂ x Z₂ ({0},+) E Z₁ Which one of the following is isomorphic to Z4 x Z6/((1,1))?

A:

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.