2 1 2.1. Given the matrix of 0 = 0 1 Prove that (OP)-¹ = P-¹0-¹. 1 3 0 and matrix of P = 2 -1 -1 2 51 3 1 1 1

Q: 3(4) 5 A = %3D -1 2

A: Here in the given question find the canonical form of the matrix A, which is P-1 A P = B   Find the…

Q: 6. 5 X•W Compute x using the vectors w = -2 and x =| - 2 - 3 2 (Simplify your answer. Type an…

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Q: -61 -2 is A- = 23 1 3 (7) The inverse of the matrix A =-2 -5 1 26 %3D 6 7 8. Truc b. Fulue

A: Given: A=13−2−2−516723

Q: 2 7 Which of the following is the matrix C that satisfies the equality (c" +312) 1 4 -1 3 (a) 2 -5…

A: We have to find matrix

Q: * For the matrix A, find det A 1. A = = | 3 -2 1 [2 |1 -1. det A = 25 O det A = -2 O det A = 1 O det…

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Q: Consider the nxn Hilbert matrix defined by 1 H = 1 13 1 n n+1 1 3 1 4 1-n 1 n+1 n+2 1 n+2 1 2n-1…

A: The answer is hij=1i+j-1

Q: 1. Two matrix vectors a and b are given as a = -0--0 and b Find (alb).

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Q: (BH) Consider the following matrix in R5×5. * 0 0 0 0 0 0 0 0 0 * A = * * * where the *s are…

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Q: 3 21 3. The all values of a and B, so that the matrix 4-3 1 4 is positive definite, are [2 B 2] (b)…

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Q: [1/V14 2/7 2/V14 -4/7 1//21 5/7 [3/V14 2/7 -2//21 [1 4 8 4//21 [14/V14 28/V14 28/V14 20 1 A : 7 = QR…

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Q: 4. (5pts) Determine if the columns of 3 -2 5 -6 -1 A -6 0 3 4 7 span R'.

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Q: (a) Show that the 3 × 3 matrix p - (4) 1 1 >= is positive-definite for p > -1.

A: A  matrix is given as follows:

Q: 1 lt 4 = [" B = [3m Jand C = [* 10" Find the matris X. + m -2 14 - m 6 аnd C — 1. Let -21 Find the…

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Q: [1 0 [9 0 01 c) A-2 = |0 4 0 Lo o 1l 9. Find a matrix A that satisfies a) (3.4) =0 -1 1 |0 0 -1| 2.

A: ANSWER :

Q: 12 6 . Determine the rank and nullity of the matrix C=|0 1

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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: 5 3 0 1 Find the size of the matrix -30 50]

A: The objective is to find the size of the matrix.

Q: 4. In fitting a straight line, the formula to find the sum of the squares of the residuals is (a) E…

A: 4. Hint: Here we need to just write the sum of the squares of the residuals.

Q: Find the rank f the Mathisx by Normal form 3 5 1. 3 13 2. 2 8.

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Q: 1(a) Two 3x3 matrices A, B satisfy the relation: A BA=6A+BA. Given: [1/3 A = 1/4 1/7 Find matrix B.…

A: Here we have det (A^-1) = 1/84. So A is invertible and A^-1 exists. Now A^-1*B*A = 6*A + B*A    Or,…

Q: 6 -4 For the matrix A find a matrix C such that C-1AC is in canonical form and 1 state the canonical…

A: Given matrix is A=6−412. We have to find he matrix C such that C−1AC is in canonical form and state…

Q: 1 Less positive Consider a symmetric positive definite matrix A separated into subblocks according…

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Q: Q: IF A=[4] and, I= identity matrix Then, Y=A² + A - 21 Find Matrix Y ? 1. [16 16] 10 2. [16 781 3.…

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Q: Q2/ Using Orthogonal Matrix 1 4 7, -8 4 If A = 4 prove that A- = A', A' being the transpose of A. 1

A: Solve by using the definition of the orthogonal matrix.

Q: 4 Apply the Cholesky factorization to A = -2 4 A = UTU. U = lo 10 x1 16 Solve A x2 = -88 by first…

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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: (1 2 3 Q15. Apply Gauss-Jordan method to find the inverse of the matrix 0 1 2 3 1 1

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Q: 2. H -1. Use the matrix formed by {₁, 2, V3} to 5 determine whether the {₁, 2, 3} spans R3. Explain…

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Q: Find the characteristic equation for the matrix A 3 0 0 A = 0 1 -1 0. 1 3 -X3 – 7X? – 16X + 12 = 0…

A: Use the method of characteristic equation to find it as in next step.

Q: Note: m=0 + m -2 6. 1. Let 1=* = l and C = |14 — т аnd C — 3 18 + m -10 -21 Find the matrix X, if A?…

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Q: 1 4 [-1 Form the Matrix Ak? 3.Let Matrix A = 2 3 and k be any scalar b = -4. -3]

A: We need to find Ak.

Q: erse of the given matrix

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Q: 2 3 1 2 and B = 2 3 0 5 [1 2-2: Let A = |1 1 |2 1 3 a) Find A-B", if exists. b) Find the matrix C…

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Q: 2 Be A, a square matrix i. Given that A holds = 44 + 5I . Prove that A is reversible, and express A-…

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Q: 5.- Let the matrix [A] be given below, obtain its corresponding matrix of cofactors. 3 -2 4 [A] =…

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Q: Find the transpose of the matrix. -2 -1 D = 1 4 -3

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Q: 9. -3 27 If A =|0 . 3 0, then show that A3 – 9A + 1013 = 4, where I3 and o -3 i. -1 are unit matrix…

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

Q: 1. Let 1 -1 3 -1 2 -1 3 -1 13 (a) Are the matrices A, B positive definite, non-negative definite, or…

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Q: Q6) Find the modal matrix P that diagonalizes the matrix (7 0 0' 0 2 0 3 A = 3 2.

A: To find the matrix P that diagonalizes the given matrix A where  A=700023032 To find the…

Q: (2) Let A be 3x3 matrix with 4|| = 4 Find : (a) det(( 3 4 )²(2 4)') ) det( 2 A + 3 adj ( A ))

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