Diagonalize the matrix A || -1 −1 1 4 16 by writing it as A = PDP-¹

Q: Find the inverse matrix of: 1 2 3 2 3 4 3 4 1

A: The given matrix

Q: Express the quadratic form (c₁r1 + c₂2+...+Cnn)² in the matrix notation TA, where A is symmetric.

A:

Q: Find the transpose of matrix A A = 4 0 -6 3 -8 1

A: Matrix transpose

Q: 1 −1 1 -2 1 2 1 −1 -1 0

A: The given matrix,The aim is to find the inverse of the matrix.

Q: [3] 37 Let A = Write 2A. Is det(2A) equal to 2det(A)?

A:

Q: Express the quadratic form (c₁x₁ + C₂X₂ + ... + Сnn)² in the matrix notation TA, where A is…

A:

Q: solve the matrix equation for X -1 1 -1 5 7 8. 3 0| X = 4 -3 1 2 -1 3 5 -7 1

A:

Q: R={(2,1),(3,1),(3,2)} as a zero to one matrix

A: Given R = R=2,1,3,13,2  we have to write it as a zero-one matrix  A= 0001001103×3

Q: 5 0 0 0 A = 1 4 -3 -1 -2 0 -3

A: A IS DIAGONALIZABLE.

Q: Find a matrix X that solves the equation 1 2 3 4

A:

Q: () Write the statement of Cayley-Hamilton theorem for square matrices.

A: Cayley-Hamilton statement

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

A: Explanation is given below..

Q: -3 -1 Find all a so that the matrix A = 1 -1 is positive -1 4

A: Matrix A is position if and only if all of the leading principal minors are positive.    Then follow…

Q: Find ∣A−1∣ for the matrix

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Q: Let A and B be n x n invertible matrices. Use matrix algebra to simplify A(A¯¹ + B¯¹)B.

A:

Q: 3 |2 -3 -47 Гз -17 The matrix product 2 4 5 |0 1 1.

A:

Q: -3-9 9 adj -2 -7 1 1 -9 -10 1

A:

Q: 1 1 1 121 N 3.

A: To Find the inverse of the matrix

Q: 1 0 2 -2 3 1 3X +|2 1 3 -1 -2 0 4 -1 5 1 5 II

A: The given equation is,

Q: find A³. Write A³ as input your answer below: all = 912 = Given the matrix 921 = 922 = ^=[83]. A A³…

A: The given matrix .The objective is to find the matrix .

Q: Find the trace of the matrix 3 A 2 -2 tr(A)

A: The given matrix is A=-332-2. Find the trace of the matrix A as follows.

Q: Find the power of A for the matrixA16

A:

Q: 7. 2 1 -1 2 Matrix + 2 Matrix -1 3 11

A: Topic:- matrix addition

Q: 2 (1 2 3 B =25 3 108 C = 2 -1 0 -4

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Q: 1 3 Find a QR factorization of the matrix A = 1 4 0 2

A:

Q: Let I be the 2 x 2 identity matrix. What is det (-41)?

A: The given data is:  I be the 2×2 identity matrix  To find det-4I Given:  I be the 2×2 I=1001

Q: Determine: 1 [1 -1 2] [2 3] +|0 1 -1

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Q: Determine the value of x, y, and z using Inverse Matrix Method

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Q: Find a matrix X = R2x2 for which −3 X¹⁹ - -24 12² -36).

A: