The rank and the nullity of A, respectively are [1 2 1 2 1 0 1 1 2 1 A 13 24 2 02242 0 0 0 0 0 "The Rank = "The Nullity= "

Q: [15 4 0 2 0 1 1 4 1 The nullity of A= Select one: а. 3 b. 1 C. 4 d. 2

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Q: 1 2 The rank of A =|0 1 is 2 4

A: We can find the rank as below.

Q: fton of a 2 5 10 12 73 21 19 45 AWhen a is -3, is b or egreater? a What is the vailue of b that g

A: We have given  b= 4a-5  We have given that value of c =-20 at a=-3  We have to check at a=-3 , is b…

Q: Let A [ - 5 13 12 13 2333 12 13 5 Explain why A-₁ = AT. -1 13

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Q: Let 1 0 -2 1 0 0 -1 -3 1 3 %3D -1 1 -1 1 3 0 -2 3 -4 Then nullity (A) O None 3 2 4 1.

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Q: 11 6 linear combinations of x, y, and z, or show that it cannot be done. Let x = 120 and z = TTTT If…

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Q: Find A V Al2) v Al3] , given [1 0 01 A = |1 0 1 lo 1 ol

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Q: The rank and the nullity of A, respectively are 1 2 2 11 0 0 10 5 0 0 4 2 0 0 0 0 a. 2,2 b. 3,1 C.…

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Q: Let a=⟨3,−5,5⟩ and b=⟨−1,5,2⟩ Find the component of b onto a

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Q: Let X = [-1 -1 1] and Y = [0 1 2] consider -1 -21 [a11 XTY = | -1 -2 а32 азз. where X' denotes the…

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Q: 1 2 If R = 3 1 that R² = 2R + cS. and S= 1 1 0 0 1 find a number c such

A: Solving matrices question by finding square of R matrix

Q: Find all numbers z such that Az3 + Bz² + Cz = D %3D B = [2 4 21 1 1 1. A = 1 3 1. 1 -2 2 4 21 C li 3…

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Q: The rank and the nullity of A, respectively are 1 2 3 11 0 0 1 5 0 0 1 2 000 0 A = a. 1,3 b. 2,2 c.…

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Q: [1 ㅇ 1 Let A = 0 -1 %3D Lo ㅇ -1] a. Compute A² and A3. b. What is A1019

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Q: 1 1 2.- 2. Is b₁ = 2 in the null space of A=-1 L-3] 1 -1 1 1 -1? What about b₂ -1 1 ГО =6?

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Q: 10 -1 o -1 If A =: 1 1 8 in null(A)? is v = 1 v is in null(A). O v is not in null(A).

A: We find whether A is in null(A).

Q: 10 Let a₁ = , a₂ = a35 , and b = Determine whether b can be written as a linear combination of a₁,…

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Q: The rank and the nullity of A, respectively are 1 2 1 2 1 0 0 1 2 1 A= 000 1 2 0 0 2 4 2 0 00 4 8

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Q: Let i = (– 4, 4, 5) and i = (6, – 3, – 2). %3D • Hint

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Q: Let A= 1 0 1 0 0101 001 1 1100 What is the rank of A?

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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

A: Given Matrix: A=14230144-10102041 To find: The determinant of the matrix. Concept used: i) There are…

Q: 2 Prove that 1 2nx 2r² > 0; where ŋy is the correlation YX YX ration Y on X and r is the correlation…

A: Answer: For the given data,

Q: max  z =  x1 + 3x2 s.t.      x1 + 2x2 ≥ 6          2x1 +  x2 ≤ 8           x1, x2 ≥ 0 For the LP…

A: A LPP is written in standard form as  max (or min) z = c1x1 + c2x2 + · · ·+ cnxn subject to a11x1 +…

Q: Let A= 1 1 Then, ||A||2= -2 Select one: а. 8+45 2 b. 7+/45 C. 10 +45 2 d. 9+45 2.

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Q: [game-tree] In the game tree show below, the first level is a MAX level, the second is a MIN level,…

A: In the alpha-beta search algorithm for a min-max tree, at every max node, the value of alpha is…

Q: Suppose a time series of returns r, follows the following recursive formula: = (1 — αL)(1 — BL³) at…

A: The question presents a recursive formula for a time series of returns, denoted by rt, which…

Q: -1 2 1 Let A Compute AAT and AT A. 1 0 1 1 -1

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Q: Is Q closed over multiplication? (Y/N)

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Q: (c) Let n be a positive integer and assume that there are integers a and b ab. Show that a < yn or b…

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Q: (b) Find the value of a4 if a, = 1, a2 = 2, and a, =an-1 + an-2 +· +a1

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Q: H.W 1.: Use Cayley-Hamilton to find 4 -1 A' and A Where A = [2 1 1 0 1 0 11 2 ]

A: Find characteristics polynomial and use caylay hamilton theorem

Q: Let A = 12 3 14 0 1 02 -3 0 1000 What are the rank and nullity of A?

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Q: 2. (6 marks) Let a, b, c € Z with a 0. Prove that if a X (a + 2b + 3c), then a Xb or a Xc.

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Q: - A = 2x(x + 3) − 3x²(x + 2) + 6x² - 9x 3x (2x - 3)

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Q: Find the null space for A. 12 0 [4] -3 -4 -1 6-6 9 A = null(A) = span 100

A: The given matrix is A=120-3-4-16-69 We have to find the null space of the given matrix.

Q: -1 1 0 -1 If A = is v = 1 in null(A)? 4 1 1 -1 O v is in null(A). O v is not in null(A).

A: Given that: A=10-1111  and v=-14-1

Q: Find the null space for A. A = 1 0 0 1 06 10 0 0 1 0 1 0 1 1 null(A) = span 0000

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Q: Given A=[1−5  1-3] compute 5A

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Q: 2.14 Use the identity EijmEkim = daðn – dad to show that a x (b x c) (a c)b- (a b)c. %3D

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let a : V → W be a linear map for vector spaces V, W over R, V₁, V2, V3, V4 a basis of V and w₁, W2,…

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Q: Find the antideviVative 2+x € ) =

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