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Matrices

Matrix operations

Given A = 1 3 -2 6 Find A^-1, the inverse of A Please show ALL work, thank you!

Systems of Equations : Real World Situations and Determinants

1. In real-world situations, what is the advantage of using the Method of Substitution to solve a system of equations rather than using the Method of Addition? 2. When solving a 3x3 determinant, we broke the determinant down into a sequence of 2x2 determinants, remembering to alternate the signs of the leading coefficients in

Matrices : Solve by Row Reduction

Please show every step no matter how minor, use the brackets for each reduction and write out every equation change. Please leave no details out. Thanks! 1) Find the general solutions of the systems whose augmented matricies are given in a) and b). What is a general solution? a)1 -2 -1 3 3 -6 -2 2 b) 1 2 -5 -

Matrices : Gauss-Jordan Elimination

65. A father, when dying, gave to his sons 30 barrels, of which 10 were full of wine, 10 were half full, and the last 10 were empty. Divide the wine and flasks so that there will be equal division among the three sons of both wine and barrels. Find all the solutions of the problem. (from Alcuin) 4, 5 Find all solutions of the

Matrices: Gaussian Elimination, Calculation Time and Cramer's Rule

Questions: a) How many multiplications are necessary to find the determinants of matrices which are 2x2, 3x3, 4x4? b) The number of multiplications for an nxn matrix may be found in terms of the number for an (n-1)x(n-1) matrix. FIND THIS FORMULA and use it to obtain the number of multiplications for a 10x10 matrix. c) Fo

Matrices : Number of Terms

The number of multiplications for an n X n matrix may be found in terms of the number for an (n-1) X (n-1) matrix. Find this formula and use it to obtain the number of multiplications for a 10 X 10 matrix

Null Hypothesis

Show that the null space of A^A coincide with the null space of A. What is the range?

Matrix System

Solve the system with the initial value... see attached. Solve the system -20 5 -20 5 with the initial value 0 -6

Question about Fields : Complex Numbers

Please see the attached file for the fully formatted problems. LET H = a b -b a : a,b is an element of C (complex numbers) Is (H, +, .) a field? If not, give reasons.

Matrices and Vectors : Linear Independence

Please see the attached file for the fully formatted problems. Let A = [ -5, 6, -19] B= [-1, 2, -3] and C= [-2, 2, -8] Determine whether or not the three vectors listed above are linearly independent or linearly dependent. **they are linearly independent*** The vectors were written horizontally this time, as they ofte

Inverse Matrix

If matrix A = [given], solve for the inverse matrix A-1. *(Please see attachment for complete problem)

Matrix Solutions

Determine the value of K for which the system has no solutions. (See attachment for full question)

Matrix System

{ x + y = 6 { 4x - 2y = 42 {10x - 2y = 96 (See attachment for full question)

Matrix Systems

Solve the System {x1 + x2 = -4 {x2 + x3 = 3 {x3 + x4 = -5 {x1 + x4 =-12 (See attachment for full question)

Matrix Systems

Solve the System { x1 - x2 - 3x3 = 6 {5x1 - 4x2 - 4x3 = 6 {2x1 + +16x3 =-36 (See attachment for full question)

Matrix System

{ 4x1 + x2 = -9 { 12x1 + 3x2 = -27 (See attachment for full question)

Matrix (Row Operations)

Solve the given system using matrices (row operations). *(Please see attachment for complete problem)