Exercise 4. Consider the matrix a A = c d = 0. (Hint: Find a lincar (i) Find a monic, quadratic polynomial p such that p(A)e1 dependence between e1, Ae1, and A?e1.)

Q: Find an invertible matrix P and a matrix C of form that A PCP-¹. = P = C = −2+ i -2- i 2 2 3+2 i 0…

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Q: - Let p(t) = t5 - 6tª + 6t3 – 6t² + 5t. a) Factorise p(t) as a product of degree 1 polynomials. b)…

A: The given polynomial is p(t)=t5-6t4+6t3-6t2+5t We have to find the roots of this polynomial to write…

Q: 4. Find the standard matrix for T where Ta2) =(2x,+x -2,).

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Q: Let A be any invertible 9 x 9 matrix. Which of the following is equal to det(Adj A)? OA. (det A) B.…

A: Given: A is an invertible matrix of order 9×9 We are required to find: det(AdjA)

Q: Let A = [ 9-8 4-3 Find an invertible matrix X such that X-¹AX is diagonal.

A: Introduction: A matrix A of dimension n x n is called invertible if and only if there exists…

Q: 2. Let a, b be non-zero real numbers. Let T be an n × n matrix. If T satisfies (Tal₁)(T - bln) = Onn…

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Q: Find the matrix A of T so that T ([]) = A[]₁

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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: 1: Which of the following vectors are linearly dependent? A: H and 3 B: 2 and 4 C: Ο Α О в O C O D 0…

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Q: Given u = [1 0 1] and v = [1 1 1]T (v is column matrix), evaluate the Boolean product u ʘ v

A: Given u = [1 0 1] and v = [1 1 1]T (v is column matrix), evaluate the Boolean product u ʘ v

Q: [1 0 1] Q2. Is the matrix A = 0 1 1 defective or diagonalizable? If diagonalizable, write the…

A: We have to solve given problem:

Q: Let a be a real number. Let 1 1 A = | 0 1 1 1 1 2 a) Find the value of a for which the matrix is not…

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Q: Find an invertible matrix P and a matrix C of form that A = PCP-¹. P= C = ? ? ? ? ? ? ? ? -1 -[27] A…

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Q: Define T: R² R² by T(x) = T I1 I2 b) Find the standard matrix A of T. 3x12x2 2x2

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Q: Let -8 0.5] -8 -3 Find an invertible matrix X and a diagonal matrix D such that X-¹AX = D. 1.88 88 A…

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Q: Suppose T: R² → R4 is a linear transformation with T(₁) - (standard) matrix A such that T(x) = Ax.…

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Q: Find the characteristic polynomial of the 3 x 3 matrix, A, where

A: A matrix is a mathematical object containing numbers arranged in rows and columns. If the number of…

Q: Define T(f) = f′ from P4 to P4. (a) Prove T is linear. (b) Give the matrix for T. Is it invertible?…

A: Let us first prove that T is linear.

Q: Consider the linear function T below. 4 T: R* → R*, X1 x1 + V5x2 X2 X2 X3 х2 — 5хз X4 -V5x4 (a)…

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Q: 2. Find the matrix A of T so that T ([]) = A[*].

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