Determine whether the following is a basis. 1.S %3D (4 - х, х3, 6х?, х3 + 3х, 4х — 1} | [2 0* [1 0. 3. l3 2! 12 2. S =

Q: If the matrix ? = [ 2 3 −1 2 ], show that ? 2 − 4? + 7? = 0.

A: From the given problem:   A=23-12   So the characteristics equation is:   A-λI=0

Q: -2 is diagonalizable. Show that B 2. Select one: 6 0 O A( 0. O B. None of the Above 6 0 1. 6. D. 0.…

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Q: С. [ E国 -18 3 7 12 13 -2 3 9 11 5 3 4 8 -3 -15 7 8 4 8 -6 2 -8 6 -2 19 -8 26 -18 16 -13 4 Matrix A…

A: A detailed solution is given in step 2.

Q: Let A = 4 (15). 5). What is the (2, 1)-entry of 4-12 6 7 ℗ INPUT HELP

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Q: x- y+10z = 29 x+ y+2=6

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Q: 1 0 0] 4 -4 -3 10 A matrix A factors into L = -2 1 0 and U = -1 3 Use this to solve Ax = 22 1 2 1 4…

A: “Since you have posted multiple questions, we will solve only first part for you. To get remaining…

Q: Let (13). Which of the following matrices is a solution X of the equation O O 4 = (1²₂3) A O and B =…

A: Topic = Matrix

Q: Simplify: -3i(4 + 2i)

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Q: ii. the missing elements of the adjoint of M, (-11 1 13 adj(M) = -9 an a2 3 a a33) :=

A: A detailed solution is given below

Q: Ex. 600. Given the 2x2 Matrix A 1 2 11 3 Determine B=A+A and C=A-A Answers:…

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Q: [ 5 8 . Determine x and y if: ]3 4] 23 34

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Q: Find the NORMALIZED Gaussian prime factorization of a. -14+102i b. 666. Also, find the number of…

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Q: N(a + bi)N(c + di) = N[(a + bi)(c+ di)] = 2. Show that 65 can be expressed as a sum of two squares…

A: See the detailed solution below.

Q: If the row exchange matrix P sends row4 to row1, then PT Oa sends row1 to row3 Ob. sends row4 to…

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Q: Find the rank of the matrix 3. 5 9 -3 5 -11-5 -3.

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Q: Express column 6 as a linear combination of columns 2, 4, and 5. 012002 4= = 2 6 7 000 106 000017…

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Q: (1 2 3 4 5 6 a = E S6 is a product of- 2-сycles. 2---- --- 4 1 652 O 2 3.

A: The given permutation is α=123456413652∈S6 We have to find the number of 2 cycles in this given…

Q: Find the following matrix product, if -9 5 6- 3 7 3D7

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Q: r1 21 [1 -2 3 5 1 3 If A = 2 2 1 -4 and B =3 4 %3D -3 -6 -2 1 1 4 -2 3 [1 3 L3 -1 2- Find the second…

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Q: Find u v, 2(u + 3v), and 2v- u. - u = (6, -5, 8, 3), (a) u-v= (b) 2(u +3v) = (c) 2v - u = v = (-2, 5…

A: The solution is shown below-

Q: Find bases for the row space and column space of A. -2 -3 -5 A 1 1 1 2 4 3 2 9 7 6 5213 2 -3

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Q: -(000 5 4. 4 1 1

A: the given vectors arev1=1-241,    v2=3-512, v3 =2-3-23

Q: [1 -2 -1] Let A- 2 4 l3 0 -2 -1 3 and B- 3 2 . Express the second column of AB as linear…

A: The objective is to express the second column of AB as linear combinations.

Q: Determine whether or not the following sets Sof 2 x 2 matrices are linearly independent. Select an…

A: Note: As multiple questions have been asked, so only first question 1 has been solved according to…

Q: Write down the quadratic form that corresponds to the following 4 -1 -3 -3 1 324

A: The given matrix is, A=3242-1-34-31. The quadratic form of the matrix A is Q(x)=xTAx, where…

Q: nts) Check the definiteness of the following matrices A and B; -1 1 1] A = |1 5 L3 0 5 0 B = 3 -1 2…

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Q: Find the transpose of each matrix.

A: To find transpose of a given matrix interchange its rows and columns  a. b.

Q: SupposeP(A) =.55,P(B) =.3,P(C) =.35, andP(A∩B) =.20. Find thevalue of each variable. Write your…

A: Given, PA=.55, P(B)=.3, P(C)=.35, and PA∩B=.20 From the given Venn diagram, PA∩B=x+0.15 ⇒x=PA∩B-0.15…