3. Consider the matrix below for this item: by A. 4 A = -4 3 -3 -31 2 -1 3.1. Write out the quadratic form generated by A explicitly. 3.2. Find the symmetric matrix B that generates the same quadratic form generated 3.3. Determine the definiteness of the matrix B using leading principal minors. (Is B positive definite? Is B positive semidefinite?)

Q: For which values of the constants b and c is the follow- ing matrix invertible? 1 b -1 -b

A: The given matrix is 01b-10c-b-c0

Q: 3 -3

A: An important fact about elementary matrices is that if a matrix A is invertible, then it can be…

Q: -10 81 O 10] B= -4 2 1

A:

Q: Let A be a 4 x 4 matrix. 1. Give a 4 x 4 matrix M that may be used to perform the row operation -5R3…

A:

Q: H5. Consider the matrix 0 c-[98] C= -1 0 First, show that C² = -I and use this relationship to…

A:

Q: Determine which of the formulas hold for all invertible n x n matrices A and B OA. (A+ B)² = A² + B²…

A:

Q: Find the matrix of the quadratic form. Assume x is in R². 9x² - 12x₁x₂ + 8x²2 b. 8x² +10x₁x2

A: The quadratic form:a) b)  To Find:Matrix of quadratic form.

Q: III. Find the inverse of the following matrices: (Apply Gauss Elimination) 1.) (0.50 3.60) 3 -1 2.)…

A: To find the inverse of the matrices.

Q: For the following matrix, do a single valid elementary row operation to get a 1 in Input the…

A: We have  41013-48 we have to get '1' at first row and first colum element.

Q: 27. For any matrices A and B for which the product AB is defined, the (i,j)-entry of AB equals a¡bj…

A: