Be A matrix 2×2 and pA the respective characteristic polynomial. Knowing that pA(A)=0, prove that the sequence (I,A,A2) is Linearly Dependent (LD), where I is the identity matrix.

Q: Question 5 Let a and 6 be positive real numbers and b + 1. Find a + bif the exponential function…

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Q: Find the transpose of the Attached matrices

A: Transpose of a matrix is obtained by interchanging the rows into columns and columns into rows.

Q: let Q(x)= x12 -8x1x2 -5x22 , then matrix A of the quadratic from is A=?

A: Explanation is given below..

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A: We have to find f(A).

Q: Find ∣A−1∣ for the matrix

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Q: Use the given definition to find f(A): If f(x) = a, + a,x + a2x + - ax is a polynomial function,…

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Q: EXER 7: MATRICES Prove that if N is invertible then MN¹ = N¹M if and only if MN=NM.

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Q: Use matrix multiplication to find the contraction of (a,b) with factor k =1 / alpha, where alpha is…

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Q: Show that ∣A∣ = ∣AT∣ for the matrix below.

A: Now the transpose is,

Q: matrix A if (A" – 21)* = } Determine the matrix A if %3D

A: Given,             12AT-2I-1=1234To find : The matrix A.

Q: Find ATA for the matrix. Show that this product is symmetric.

A: The transpose of matrix A is,

Q: For each 2 x 2 real matrix A find the canonical form B and an invertible matrix P such that P-1AP =…

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Q: Determine all the n × n− matrix A with the range such that A2 = A.

A: Clearly the zero matrix and identity matrix are the trivial examples of our problems. However there…

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Q: Use matrix multiplication to find the dilation of (a, b) with factor k = α, where α > 1

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Q: Let z be a real number and let A be the matrix 2 I A - (-34). -2 i. Find all values of r such that A…

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Q: please continue matrices and find for x, y, and z cramers rule

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Q: 0 0 1 -1 0 0 -1 2002

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Q: Find a formula in terms of k for the entries of AK, where A is the Hermitian matrix below 13 4 9. 9.…

A: Here , A=-139-49+2i9-49-2i9-149 The characteristic equation of A is…

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A: Interpolation is done for obtaining a polynomial from the discrete data. When these data are plotted…

Q: Let A be a 4x4 matrix and det(A)=2. Find det(2A-)'

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Q: the acdjainbaf square of As of 2.

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Q: Find the characteristic polynomial of the matrix -3 1 A = -3 -1 -3 -4 p(x) =

A: Given problem is :