Explore BrainMass
Share

# Linear Algebra

### Non-linear Differential Equation Word Problem

Two chemicals A and B are combined to form a chemical C. The rate of the reaction is proportional to the product of the instantaneous amounts of A and B not converted to chemical C. Initially there are 40 grams of A and 50 grams of B, and for each gram of B, 2 grams of A are used. It is observed that 10 grams of C are formed

### Basis and basis matrices

3. Let B1 = {v1,v2,v3} be a basis of vector space V and B2 = {w1,w2,w3} where w1=v2+v3; w2=v1+v3; w3= v1+v2 Verify that B2 is also a basis of V and find the change of basis matrices from B1 to B2 and from B2 to B1. Express the vector a(v1) +b(v2) + c(v3) as a linear combination of w1,w2,w3

### Linear algebra

Please help with the following problems. 1. Let u1 = (1,2,1,-1) and u2 = (2,4,2,0). Extend the linearly independent set {u1,u2} to obtain a basis for R4 (reals in 4 dimensions) 2. Let U1,U2 be two subspaces of a finite dimensional vector space V such that U1+U2 = V. Prove that there is a subspace W of U1 such that W (+)

### Linear Functionals Complex Matrices

(See attached file for full problem description with symbols) --- If A and B are complex matrices, show that is impossible. ---

### Systems of Three Equations with 3 Variables ( 3 Equations and 3 Unknowns )

Please help me solve the following system of three equations and discribe the methods that are being used to help me understand: X + Y + Z = 6 2X - Y + 3Z = 8 3X - 2Y - Z = -17 Thank you!

### Linear Differential Equations : Solving by Change of Variables - Changing an Independent Variable

Please see the attached file for the fully formatted problems.

### 1. Solve this system of four equations: (see full description) 2. If x varies directly as 2y-1, and x=9 when y=2, find the value of y when x has a value of 15

1. Solve this system of equations. Put your answer in alphabetical order. 5w+3x-y-z=-2 w+x+y+z=2 2W-x+y+4z=0 3w+2x+3y+2z=1 2. If x varies directly as 2y-1, and x=9 when y=2, find the value of y when x has a value of 15.

### Linear Algebra : Linear Transformations, Vector Space and Basis

Let C^2x2 be the complex vector space of 2 x 2 matrices with complex entries. Let B= [1 -1] [-4 4] and let T be the linear operator defined on C^2x2(T: C^2x2 --> C^2x2) by T(A)=BA. What is the ra

### Numerical Linear Algebra: Complex nxn Matrix

Let A = (aij ) be a complex n × n matrix. Assume that h Ax, x i = 0 for all x Є C n . Prove that (a) aii = 0 for 1 ≤ i ≤ n by substituting x = ei (b) aij = 0 for i 6 = j by substituting x = pei +qej then using (a) and putting p, q = ± 1, ± i (here i = √- 1) in various combinations Conclude that A = 0.

### Linear Algebra : SPD Matrix and Inverse

Let A be a symmetric and positive definite (SPD) matrix. Is A^-1 ( inverse of matrix A) a SPD matrix? If so, prove it. If not, explain and give an example.

### Determine if Two Equations are the Same

Are the two equations the same. If so verify (see attached). σ^2 = Σ ((x[i]-bar-X)^2)/n and σ^2 = Σ (x[i]^2)/n - bar-X^2

### Systems of Linear Equations, Row Echelon Form and Number of Solutions

True or false 1. Every linear system of four equations in five unknowns has infinitely many solutions. 2. If two systems of linear equations have augmented matrices that row reduce to the same reduced row echelon form, then they have the same solution set. 3. If a system of m linear equations in four unknowns has a uniq

### State-Space Model

Obtain a state-space model of the system shown in Fig. 3 (see attached file).

### Linear Algebra Explanation

Hello all! I humbly apologise in advance if I'm posting inappropriately, or asking for a solution that is technically beneath you. Problem is as follows: "When Mary was half as old as Sam was when Mary was as old as Sam was when Mary was as half as old as Sam is now, Sam was four times as old as Mary was when Sam was

### Numerical Linear algebra. Gram-Schmidt orthogonalization.

See attached file for full problem description.

### Orthogonal Matrix and Eigenvalues : Let A be a 3 x 3 real orthogonal matrix with det A = 1. Prove that &#955;= 1 is an eigenvalue of A.

Let A be a 3 x 3 real orthogonal matrix with det A = 1. Prove that &#955;= 1 is an eigenvalue of A.

### Numerical Linear Algebra/Norms

Based on the parallelogram law, show that the norms ||.||_1 (1-norm) and ||.||_infinity (infinity or maximum norm) in R^2 are not induced by any inner product. Parallelogram Law: ||u+v||^2 + ||u-v||^2 = 2||u||^2 + 2||v||^2. ||x||_1: = sum i = 1 to n of |x_i| ||x||_infinity := max ( 1 =< i =< n)|x_i|.

### Numerical Linear Algebra. Norms.

Find two norms on the space C[0,1] that are not equivalent. Justify your answer. ( Please prove that the example you provide is a norm on the given space and show that the 2 are not equivalent.)

### College Algebra Functions and Graphs

1. To prepare, you must perform the following tasks: The following data was retrieved from www.cdc.gov. It represents the number of deaths in the United States due to heart Disease and cancer in each of the years; 1985, 1990, 1995, and 2002. Year Disease 1985 1990 1995 2002 Heart Disease 7711

### Linear equations

It is approximately 300 miles from Chicago, Illinois, to St. Louis, Missouri. Allowing for various traffic conditions, a driver can average approximately 60 miles per hour. How far will I need to travel to reach St. Louis after I have traveled 3 hours, and write a linear function that expresses the distance to be traveled to r

### Solve Systems of Equations : x + 3y = 12 and 4x - y = -17

The solution to the system of equations x + 3y = 12 4x - y = -17 is: A. (3,3) B. (12, -17) C. (-3,5) D. (5,3)

### Find the linear Equation relating book value and number of years.

An item costs \$1300, has a scrap value of \$100, and a useful life of six years. The linear Equation relating book value and number of years is: A. BV = -100x + 1300 B. BV = -100x + 1200 C. BV = -200x + 1200 D. BV = -200x + 1300

### Problem : An item costs \$900, has a scrap value of \$50, and a useful life of five years. The linear equation relating book value and number of years is:

An item costs \$900, has a scrap value of \$50, and a useful life of five years. The linear equation relating book value and number of years is: A. BV = -50x + 850 B. BV = -50x + 900 C. BV = -170x + 850 D. BV = -170x + 900

### Solve Simultaneous ( Systems of ) Equations

Solve for x and y in the following two sets of simultaneous equations: 4x-2y = 1 ......(i) 8x-4y = 1 ......(ii) y = 2x + 3.......(i) 2y - 4x = 6 .....(ii)

### Current Electricity: Kirchhoff's Laws (ully explained)

(See attached file for full problem description) --- 2. Finding Unknowns Determine the unknowns in the circuit shown in Fig.3. How do electrical engineers use Kirchoff's current law and Kirchoff's voltage law to write a system of linear equations? ? Based on your explanation, write a system of linear equations for Pro

### Least squares solution

Using the least squares method answer the following in a word doc. · What are the main strengths of this method? · What are its main shortcomings? · When would least squares be useful in the real world? · Does the use of linear algebra make this method easier to understand or use?

### Systematic Elimination method to solve the system

Use the Systematic Elimination method to solve the system of ordinary differential equations. See attached file for full problem description.

### Linear problem

I think the answer to this problem is true because 2x1 comes first and that coincides with 200. If I am wrong please explain. The question is The constraint 2x1 - x2 = 0 passes through the point (200,100). True or False.

### Numerical Linear Algebra : Unitary and Triangular Matrices and Krylov Matrix

1. Let A = QR be the factorization of a A into the product of a unitary matrix and a trianglular matrix. Suppose that the cloumns of A are linearly independent. Show that |rkk| is the distance from the k-th column of A to the linear space spanned by the first k-1 columns of A. 2. Let A &#1028; C^(mxm) and b &#1028; C^m be abi

6x-7y=8 -5x+2y=1