Consider the following matrix 1 A 8 5 -3 5 -1 -3 -1 5 (a) State whether the matrix is positive or positive semi-definite (b) Show that the matrix is singular or non-singular. (c) Is r (A) = tr (A)? Substantiate your answer.

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

A: The given matrix

Q: 3. (a) Solve the matrix equation for X: -1 0 1 1 2 1 1 -3 1 -1 3 1 -1

A: If Ais a m×n matrix and B is a n×p, then AB is m×p Hence here X is 2×3 Let X = abcdef Thus…

Q: [2 -1 1] A = |1 1 2,x = |y| and b = |b2 [-1 5 4] a. Determine if the columns of the matrix A span…

A: We have to determine  whether the column of matrix A can span R^3

Q: First question: Find the inverse and determinate of the matrix A = [??H] -1-3 1 3 60 1 0 1 ||

A:

Q: Evaluate ff 3xdA where R is the region shown. 3. YA 2 4 -2 0 R 24x

A:

Q: 20. The following are rules of transposition of a matrix except: (explain) a. (A")" = A b. (A + B)"…

A:

Q: Let A and B be 2 x 2 matrices with real entries. Determine if the following statements are true or…

A: We will find out the required solution.

Q: What is a, if A = 2 4 is a singular matrix ? a Simplify (1+x)(1+x²)(1 – x + x?) in descending order…

A:

Q: Find matrix such that 5 3 -1] X+ 2 -3 1

A:

Q: PS2.5 Use the definition of Ax to write the matrix equation as a vector equation, or vice versa. (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

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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: (A-¹) = (A¹) (assuming A- exists) (AB)−¹ = B¯¹A−¹ (assuming A-¹ and B-¹ exist)

A:

Q: Q(x1,X2, x3) = 2xỉ + 3x3 – x + 5x1x3 + X2X3

A: Given,        Q(x1, x2, x3)=2x12+3x22-x32+5x1x3+x2x3

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

A: The given matrix,        21-13+2-1211

Q: Use elementary row operations to determine A-1 (you should be able to do (a) elementary row…

A: 1.a A=123-111201A=11-0-2-1-2+30-2     =1+6-6     =1determinant of A is not zero, therefore inverse…

Q: (b) Table Q4(b) is generated from the function ƒ(x)= e* - 4x² + B , where B is the last two digits…

A: Given: fx=ex-4x2+B To find: f'1.5

Q: ( -10! BIf (21-A)-! evaluate the matrix A.

A:

Q: Determine the value of x so that the matrix is singular (does not have an inverse) Which is the…

A: Note that, the matrix is said to be singular if the determinant of the matrix is 0.

Q: Use Gauss-Jordan to find the inverse of the matrix A given by -3 0 0 2a b a A = 10 0 2 What are the…

A: Gauss Jordan’s Matrix Inversion method. In this method we shall find the inverse of a matrix…

Q: How do you know whether a matrix is invertible?

A:

Q: How to make this matrix diagonally dominant?

A: A square matrix is said to be diagonally dominant if for every row of the matrix, the magnitude of…

Q: Let matrix A = 1 1 1 3 2 1 −2 3 1 (a)Find two distinct row echelon forms of A. (b) Find the…

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Q: 1 6. Given that A = -1 and B = Which of these matrices equal (AB)'? -2 0 (c) 0. (a) 0. (b) (d) -2 -2…

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Q: True or False The identity matrix has properties similar tothose of the real number 1.

A: We have to say that the given statement is true or false: The identity matrix has properties similar…

Q: for a matrix A 3 6 2 5 if f(x)=(x+2)(x-2), calculate f(A)

A: Given: Matrix A=3625 To Find: f(A) when f(x)=(x+2)(x-2)