ГО 5 4 5 1 2 2 3] A = [1

Q: Use the inverse matrix method to solve Ax = b below X = (x, +2x, = 3 (2x, – x, = 1

A: Given that  To solve the given system by using inverse matrix method. X1+2x2=3 2x1-x2=1

Q: Which matrices have negative eigenvalues?

A:

Q: can you show part b) closed under scalar multiplication with matrices?

A:

Q: Give an example of a 3x3 matrix with eigenvalues 0,1,2

A:

Q: Give an example of a 3x3 non triangular matrix with with eigenvaluse 2,3,-2

A: Give an example of a 3x3 non triangular matrix with with eigenvaluse 2,3,-2

Q: Explain why a symmetric matrix with real entries can't have complex eigenvalues.

A:

Q: 2x₁ + 4x₂x3 = 15 7x₁3x₂ + 3x3 = -4 4x13x28x3 = 19

A: Given: 2x1+4x2-x3=157x1-3x2+3x3=-44x1-3x2-8x3=19 We have to find the inverse of the coefficient…

Q: Let A, B, and A+B_ all be square invertible matrices of the same size. Show that (A +B')' = A(A+B)'…

A:

Q: Let A, B, C be invertible n x n matrices. SOLVE for A in: A^-1B^-1 = C^-1

A:

Q: Find a real matrix A such that A ^6 = (09, -90)

A:

Q: a) Decompose the coefficient matrix A into lower and upper triangular matrices.

A:

Q: Use the Gaussian algorithm to determine the inverse matrix A^-1.   A = 1  2  1 0  1   3 2  4   1

A:

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

A:

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

A: