### Find the Inverse of a Matrix

Please solve for the following: Matrix row 1 = [1 .5] row 2 = [0 .5] Task: Find the inverse.

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Please solve for the following: Matrix row 1 = [1 .5] row 2 = [0 .5] Task: Find the inverse.

Multiply matrix a by matrix b matrix a: row 1 = [0 1 2] row 2 = [-1 4 .5] row 3 = [1 3 0] matrix b: row 1 = [3 -1 5] row 2 = [0 2 2] row 3 = [4 -6 0]

Multiply Matrix[4 -1] over [2 .5] by matrix [3] over [2]

Let AX =C, If B is the inverse of A, then the solve the matrix X Matix B(3x3)row 1 = -17 78 24 row 2 = -3 13 4 row 3 = -10 16 5 Matrix C(1x3) row 1 = 24 row 2 = -686 row 3 = 2246

#5 M is a (3*3) matrix, use the identity matrix to find the inverse of M= 1 5 42 -7 -34 -287 28 136 1149

Please see the attached file for the fully formatted problems. Let K be an nxn matrix and .. a small number. Imitating .... valid for small x, it is natural to define .... Explain why this makes sense. Prove trace log... = log det.... Still with ... small so that everything makes sense.

Please answer the following question: Find an adjacency matrix for Cn. (That's C 'sub' n)

Attached deals with the orthogonality of the eigenfunctions of the self adjoint operator.

Diagoalize te given matrix: A= 3 1 1 1 0 2 1 2 0 an find an orthogonal matrix P such that P'-1(Pinverse)AP is diagonal.

Verify that P= 2/3 -2/3 1/3 2/3 1/3 -2/3 1/3 2/3 2/3 is orthogonal matrix.

Find formula for the volume enclosed by a hypersphere. See attached file for full problem description.

Determine the characteristic values of the given matrix and find the corresponding vectors: [ 1 -2 ] [ 2 -3 ]

What is the symmetric matrix of the quadratic form 2x^2 - 8xy + 4y^2?

Please see the attached file for the fully formatted problems.

Find the value of each of the third-order determinants:  2 0 -2   1 1 5  (this is a  3 4 5  3x3 matrix)

Please see the attached file for the full problem description: 1. Show that if   0, then A^-1=1/ [ d -b ] [ -c a ] . Help: : is the determinant A [ d -b] [ -c a ] : is a 2 x 2 matrices

Solve the following system of equations by performing elementary row operations on the augmented matrix. x1-2x2 +2x4 = 6 2x1-4x2+x3-x4 =-2 3x1+6x2-x3-x4=-4 x1-2x2+x3-3x4=-8

Linear Algebra Matrix of the Linear Map Basis of the Linear Space Let T be a linear map on R^2 defined by T(x,y) = (4x - 2y, 2x + y). Calcu

Solve using the Gaussian Elimination and show all work. Mike, Joe and Bill are Painting a fence. The painting can be finished if Mike and Joe work together for 4 hours and Bill works alone for 2 hours, or if Mike and Joe work together for 2 hours, and Bill works alone for 5 hours, or if Mike works alone for 6 hours, Joe works

Consider the matrix a=(1 1 2 1 2 -1 3 2 1 5 5 2) Find N(A), R(A), N(A^T),R(A^T). Show that the fundamental subspace theorem holds: N(A^T)=R(A)^(upside down T), N(A)=R(A^T)^(upsidedown T). Hint: Notice that the fourth row is the sum of the first three rows.

Investigate the Automorphism Group of Z_p + Z_{p^2}. Please see the attached file.

Using the method of undetermined coefficients, find the solution of the system: X'=AX + B that satisfies the initial condition: X(0)=( 0 1 -1). A and B are matrices defined in the attached Notepad file. Note: When solving the homogeneous soln, exhibit a fundamental matrix psi(t) and al

Prove that for any self-adjoint bounded linear operator T on a Hilbert space H that (Tf,f) is real-valued for all f in H.

If A is a 3x3 matrix such that the determinant A is 2 and A1 is the transpose of A, find the determinant of A1.

Find the inverse of the following 2x2 matrix: | 1 2 | | 3 4 |

Find the matrix products.

Please see the attached file for the fully formatted problems. Solve the following matrix problems.

Please see the attached file for the fully formatted problem.

17. Solve the system of equations by the Gaussian elimination method. x- 3y + z= 8 2x- 5y -3 z= 2 x + 4y + z= 1 18. Find the inverse of the given matrix. 1 2 -2 -3 19. Evaluate the determinant by expanding by cofactors. -2 3 2 1 2 -3 -4 -2 1 20. Solve the system of

Prove or disprove that, for matrices A,B,C for which the following operations are defined: a. A*(B+C) = A*B + A*C b. A+(B*C) = (A+B)(A+C)