(3) A square matrix A is said to be nilpotent, if some power of it is equal to the zero matrix, that is Ak = 0, where k is the smallest postive integer that satisfies the equation. Let A = 0 2 3 004 000 (a) Find the value of k for the nilpotent matrix A. (i) 0 (ii) 2 (iii) 3 (iv) 4 (v) None of the above (b) Compute e. Select the correct answer. (i) (ii) (iii) (iv) A = A = 0 0 4 000 00 0 27 004 -6 A = 0 0 0 1 2 7 0 --(14) A = 0 001 0 2 11 0 4 -(9) 0 0 (v) None of the above

Q: For each of the following, factor the matrix A into a product QDQ" where Q is orthogonal and D is…

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Q: Q.1/ (7+7) Marks A- Use matrix inverse to solve the following system of equations: 4x + 6y + 2z = 28…

A: Image is attached with detailed solution.

Q: 2. (i) Find a matrix X such that (ii) Find a matrix Y such that 1 - 32] x = [3] X -2 21 53 Y = 0 2²…

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Q: Find the RREF of the matrix -4 1 -3 من که من 2 3 -1 4 -2 3 2

A: to find the row reduced echelon form of -4       31      - 1-3       42       - 23        2

Q: 21

A:

Q: 1 2 5 -3 Find a matrix X that satisfies XA=B, where A = and B = 2 5 3 -5

A: We find inverse of A then fin matrix X.

Q: (-1 3 2 Find the polynomial of a square 3×3 matrix A=| 1 0 -2|given that -3 1 P(x) =14+19x– 3x² –…

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Q: (e) A = ; 10 2 (f) A represents the quadratic form g(x, y) = x² + 4xy + 4y²;

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Q: What is a, if A = 2 4 is a singular matrix ? a Simplify (1+x)(1+x²)(1 – x + x?) in descending order…

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Q: [2 1 Q1 \a: find the inverse of the Matrix A= 1 1 2 1 -1

A: Given Matrix

Q: Consider the matrix 3 2 - А — 1 2 1 5 2 - 1 | Use Gaussian Elimination to find the inverse of the…

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Q: (b) For the matrix A= (1) (ii) det (4) 3 27 16 [56] find:

A: Given :A=3216

Q: 2 1 0 0 0 2 0 1 3. Let A and Ba 4 x 4 matrix with det(B) = 3. 0 3 1 -1 2 0 1 (a) (3 marks) Find…

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Q: If A = [1 2 3], which type of the given matrix A ?

A: Given Matrix A=[1  2  3 ]1×3  Here number of row=1  Number of columns=3

Q: Solve this matrix question

A: Step 1:Step 2:

Q: 1 3 3 - 4 1 A(x)=x² – A -2x+3 5 2

A:

Q: -3 -2 -3 17. Find the inverse of the matrix A= 5 3 5 2 1 1

A: Given A=-3-2-3535211 The inverse of A is given by A-1=1Aadj A A=-3(3-5)-(-2)(5-10)-3(5-6)…

Q: Find (IM)1 and X. 0.7 0.2 13 M = |; D = 0.1 0.4 28 Calculate (IM)- 1. Select the correct choice and,…

A: Step 1:Identity matrix is :I=[10​01​]Given matrix is :M=[0.70.1​0.20.4​] Step 2:Then,…

Q: you explain this part? I'm finding myself confused as to how you got the 1/3 [2 -1, -1 2] matrix

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Q: = 5.8. Let f₁(x) = x³ x² +1, f₂(x) = x³ + x² + x and f3 (x) = x³ + 2x²+3x+1 be three polynomials in…

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Q: Let A be a 3 x 3 matrix with det(A) = 0. Determine if each of the following statements is true or…

A: Since, you have posted a multiple parts question. But according to guidelines we will solve first…

Q: 5 10 √2 (h) A = 10 2 α ; discuss your answer in dependence on the value of the parameters √2 a a,…

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Q: Find the matrix corresponding to the quadratic form Q(x) = x + 2x1x2 + 2x1x3. Is Q positive…

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Q: Illustrate the Gersgorin theorem by the matrix 2 1+ 2i 0 A = -1 -2 – 2i 1/4 1/41/2 140 12 1/7 1/2…

A: We state the theorem and explain it with the help of the given matrix A.

Q: +2 17 8 -4.5]

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Q: (1) Show that I + Y X is also invertible. (2) Show that Y (I + XY )−1 = (I + Y X)−1Y .

A: This is the problem of Linear Algebra, Linear Transformation. Given: X is a m×nmatrix and Yis a n×m…

Q: (c) Consider the quadratic form f(x1, x2, x3) = 3(a₁x₁ + a2x2 + a3x3)² = 4(b₁x₁ + b₂x2 + b3x3)². (i)…

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Q: 1 0 (¹²2₁) 1 1 of the matrix B x A? Let A = 00 01 02 03 O-1 O-2 O-3 and B = 2 1 (GD -1 0 1 What is…

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Q: Suppose that 2 3 Solve the linear system Ax = b for each of the following matrices b: 8 (b) 15 (a)

A: Given: A-1=1213 (a) Ax=bx=A-1b Substitute the respective values. x=121346=4+124+18=1622 Therefore,…

Q: If Y = X(XTX)-¹XT where X is a square matrix and (XTX)¹ exists, then: Statement I: Y is a square…

A: Statement I :Suppose  is a    matrix.Here,                        ( since )               (By…

Q: (b) Solve for the matrix A if given 33(2A- 31)

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Q: x-2 1. A= 3x-6 4x-11 Given that the matrix A is singular, find the possible values of x.

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Q: (a) In the downtown section of Vijayawada two sets of one-way streets intersect. The average hourly…

A: To solve (a) In the downtown section of Vijayawada, two sets of one-way streets intersect as shown…

Q: Example 4: Find the matrix that can cause widening by 4 in the direction of the X-axis and deflation…

A: Matrix is widened by 4 in X-axis and is deflation by 0.25 in Y-axis.

Q: In the downtown section of Vijayawada two sets of one-way streets intersect. The average hourly…

A: Given: The traffic chart and the quadratic equation 3x12+10x1x2+2x22. To find: (a) Amount of traffic…