3 2-1 The minimal polynomial for the matrix A = 3 8 -3 is ... 3 6 -1 Am(A)=A2-81 + 12 ○ B. m ( λ) = λ¹³ — 8λ + 12 OC. m (1) = (1 − 2) ² (1 – 6) OD. None in the given list. O E. m(1) = (1-2) (1-6) ² 27

Q: 3125 Evaluate the determinant of the inverse of the matrix A= 0 201 0014 0002] O 12 1 12 8. None of…

A: the given matrix is: A=3125020100140002 we have to evaluate the determinant of the inverse of matrix…

Q: Which of the following matrices corresponds to the elementary row operation 3R1 + R2 → R2 on.a 3 x 3…

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Q: 1. Given the matrices A = a. |A| b. B c. AB d. |AB| 302 e. Verify that |AB| = |A||B| 121 01 1 and B…

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Q: 22. 4x² + 12x₁x₂ + 13x² = 16 23. - 11x + 84x₁x2 + 24x² = 156

A: We have to proved that quadratic form is positive definite or indefinite.The matrix is positive…

Q: 1. Find the determinant of the following matrices by using elementary row operations. 4 -7 9 1 6.…

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Q: Prove the following properties of matrix addition and scalar multiplication, where A, B, and C are…

A: Use the properties of matrices to prove this statement.

Q: 3a A transformation is defined by the 2 x 2 matrix -a b - a A la +b a where a and b are scalars. If…

A: 3.a.  Given that A=-ab-aa+ba To prove: An=bn-1A is true for odd integers n by the principle of…

Q: 2.3 Find the determinant of the matrix B below  B = ( 2 1 1 0 5 −2 1 −3 4 )

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Q: 13. Find two zero divisors of the ring of 2 × 2 matrices where none of the entries are zero.

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Q: The commutator [X, Y] of two matrices is defined by the equation [X, Y] = XY - YX. Two anticommuting…

A: Given, The commutator X,Y of two matrices is defined by the equation X,Y = XY-YX. A2 = I, B2 = I,…

Q: (b) Compute the characteristic polynomial for the following two matrices: 0 1 D = (₁-²). E = (1 ²²³)…

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Q: 2. If the characteristic polynomial of a matrix A is p(2) = 23 - 522 + 62. Then tr(A) = None -5 O 1

A: Solve

Q: For the following matrix 2 6 4 3 A = 17 11 4 -1 -19 -11 -3 -1 -1 -1 1 find the geometric…

A: The eigen values of a matrix A is those values of λ which satisfy the equation A-λI=0. There exists…

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

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Q: Let A be an Xn matrix satisfying A-34 +I= 0 where 0 is the nXn zero matrix. Then A = A² - 31, A= =…

A: The objective is to choose the correct option for inverse.

Q: 1. Evaluate det 010 3 -12-3 4 0502 by cofactor expansion about a row/column of your choice.

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Q: 13. Find the inverse of the matrix * 1 2 A = -2 -2 5

A: Inverse of matrix is defined only if determinant of matrix is non-zero. A-1=Adj(A)|A| Adj(A) is…

Q: 2.1. Prove that B Is erse of A -17 11] -7,B: 0 3 2 [1 1 2 2 4 -3 [3 6 -5] 2 A = -1 11

A: To prove that B is the inverse of A.

Q: 3 4 Find the characteristic polynomial p(A)of the matrix A = Op(A) = 12 ++6 Op(A) = x? +A– 10 Op(A)…

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Q: A = 1 0 -1 Lo 0 -2 -3 -2 -2 1 3 3 -2 4 4 0 0 -1

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Q: 1 2 1. Find the inverse of the matrix A = 2 1 4 4 5 10

A: Note: - Since you have asked multiple question, we will solve the first question for you. If you…

Q: Let C2,2 be the set of 2 × 2 matrices with complex coefficients, and define the map a 0 T: C2,2 C2,2…

A: Let C2,2 be the set of 2×2 matrices with complex coefficients. Define T:C2,2→C2,2 by

Q: 1 -1 1 1 1 3 -1 1 Let, A = -2 1 4 -1 3 3 -1 -5 1 -6 a. Find a 5x5 matrix B such that AB = 0, where 0…

A: The matrix given is as follows: A=10-121-113-10-214-133-1-51-6 (a) We will apply row elementary…

Q: Y1 y2 y3 y4 ys Y1| 0.9 0.3 0.4 0.1 0.2 0 1 0.7 V2| 0.2 1 0.8 R, (x, y) = x, 0.3 0.5 0 0.2 R, (y, z)…

A: Given data:                       y1   y2 y3y4 y5R1x,y=x1x2x30.10.2010.70.30.500.210.8010.40.3…

Q: What is the det(A) if a matrix has p(A)=13 - 212 -A +3 as its characteristic polynomial. O A. -2 В.…

A: Proceed as shown below...

Q: 1 -1 Let C = 0 0 1 0. The characteristic polynomials of both these 0 2 02 matrices is p(x) = (x −…

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Q: 1. How do we denote a general m x n matrix A algebraically? What notation do we use for the (i,…

A: A system of mn number (real and complex) arranged in rectangle array in m horizontal lines (called…

Q: Question 2. Let A be a matrix in M14 (C) such that • The minimal polynomial of A is (X-A₁)²(X-2)…

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Q: Let [5 -3] A = [1 -3 – 2k] В — k 6+ 5k Find the elementary matrices E, and E2such that B = E2E¸A.…

A: An elementary matrix is a matrix which differs from the identity matrix by one single elementary row…

Q: Which of the following is the elementary matrix corresponding to the operation -2R2+R3 ? O[10 0 0 1…

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