(6) (Section 3.7 # 13) Let A and B be 3 x 3 invertible matrices so that: 0 1 1 1 в-1 0 1 0 A-1 -1 -1 0 1 1 C -1 Without computing A or B, determine the following: (a) rank(A) (b) The solution to: Bi = (c) (2BA)- 1 (d) The matrix C so that ACB 313 0

Q: 8. Find a fundamental matrix of the system y' = Ay if o\ A= 0 -2 0 -2 -2 1 1 and check your answer…

A: Explanation of the solution is given below....

Q: [2 8) Use the Gauss-Jordan method to find the inverse of the matrix A: %3D

A:

Q: Suppose A is the 3 x 3 zero matrix (with all zero entries). Describe the solution set of the…

A: To prove  Ax = 0

Q: Show that no 2 x 2 matrices A and B exist that satisfy the matrix equation [1 0 0 1 АВ - ВА. %3D

A: In this question we have to prove that no 2×2 no matrices the given matrix equation.

Q: Determine the dimension of the matrix. 0 7 15 0   −3 0 3 3 −1 1 6 7

A: Explanation of the solution is given below....

Q: At Compute the matrix exponential e for the system x' = Ax given below. x₁ = 37x₁ - 36x₂, x 2 = 34x₁…

A:

Q: Find a 2 x 1 matrix x with entries not all zero such that 2 Ax = 3x, where A = 1 2

A: Given matrix is A=2   11   2 and condition is Ax=3x

Q: Find the greatest value of A that make the matrix 2 – A 2 A singular. -6 5 – A

A: Eigenvalues and determinants

Q: In the matrix equation (3A + XB) T = - (2X) T + B matrices A, B and X are matrices of Adequate…

A: Given, 3A+XBT=-2XT+B By right distributive law, 3AT+XBT=-2XT+B Rearranging the above equation we…

Q: (4) For the zero-one matrices A = and B = calculate %3D 0 0 1 1 (а) АЛВ (Ъ) АоВ (с) ВОВ

A: 4) Note:  AΛB = [aijΛbij] =[aijbij] , known as meet of A and B, only possible if matrix have same…

Q: Assume the invertible matrix A satisfies 10 4 1 1 A 6 A 1 A 1 3 4 -1 -1 -1 1 1 5 -2 1 1 3 4 -3 -1 1…

A: Detailed explanation mentioned below

Q: If A is 3 x 5 matrix with rank 1, then the number of special solutions to Ax = 0 is %3D O is

A: Since the rank of the matrix = 1. So the number of free variables = 5 - 1 = 4.

Q: 3. Let A [1.1 -0.1] [0.3 0.7 0.7] Is matrix A invertible? How do you know?

A: An invertible matric is a matrix  for which matrix inversion operation exists . A matrix is said to…

Q: 4. Find the cofactor matrix for the matrix. 5 9 1 8 5 6 4

A:

Q: Naive Gauss Elimination Method is used to solve a set of equations given by the matrix form…

A: Round-off errors depend on the fact that practically each number in a numerical computation must be…

Q: 3 0 0 0 1 1 is an elemanter matrix. |\ 0 1 Choose one: true false

A:

Q: 17. Perform Gaussian Elimin ation on the matrix. [1 4 36 -1 -1 2 4. 0 4 -3-15 6,

A:

Q: Solve the initial value problem for the linear system æ' = Ax in dimension 3, where 7 -1 -1 A = |1 5…

A: To solve the initial value problem

Q: A n x n Hermitian matrix contains exactly k real entries. Show that k + n must be even.

A:

Q: *New Text Document (2).txt - Notepad Edit Format View Help Ln 84, Col 1 100% Windows (CRLF) UTF-8…

A:

Q: 4) (From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Section 1.5., # 24, or from your…

A: see below the answer and explanation

Q: 4. Find the vector form of the general solution of the linear system х, + 2х — хз + 3x, 3D 4 X1 –…

A: Augmented matrix of given system is 12-131-31-1221-1:4-34 After row elementary operation, we get…

Q: 1. Show that the matrix 2 1 A = 1 2 -1 -1 is positive definite.

A: Given :- a matrix A  We need to show that a matrix is positive definite. We know that , A symmetric…

Q: TRUE or FALSE: Every invertible n xn matrix is similar to the identity matrix In.

A: To state true or false given statement.

Q: Verify by direct calculation that the matrix -2 -3 -1 A = 1 %3D 3. 3. satisfies the Cayley-Hamilton…

A: by cayley Hamilton theorem , " matrix satisfied its own characteristic equation " now to satisfied…

Q: Given A = 1 1 0 3 Compute 5A *Matrix

A:

Q: Let A and B be n×n matrices. If AB is invertible, show that both A and B are invertible

A: We prove it using Theorem 2.4.5, using the following statement. 2. The homogeneous system Ax = 0 has…

Q: 2. Construct a 4x4 nonzero matrix A such that the vector -3 is a solution of Ax= 0. -4 2.

A:

Q: Let A be 5x1 matrix. Knowing that Rank (A) = 2. Then Nullity(A) is equal to: O 2 ONone of these

A: The solution is given below in the next step:

Q: The order of the single matrix obtained from 1 1 -1 To 1 23 is 1 0 21 -1 0 2 2 0 3 2 (a) 2 x 3

A: Here the order of the matrix needs to find out for both terms. Subtraction and addition won't affect…

Q: There is a unique value of h such that the matrix 2 3h/2] -1 3 1 h 4 0 h+1| is NOT invertible. Find…

A:

Q: 1 Problem 2. For a nonsingular matrix A and nonzero scalar ß, show that (BA)- =A-. Problem 3. Prove…

A:

Q: 2 x + y + z = 2 −3x+3y−3z= 9 −x +7y +3z = −11 Compose the augmented matrix corresponding to this…

A:

Q: Consider the elementary matrix 1 0 -- a 2 1 Describe the action of this matrix from the left in…

A: Here →A=(1,2),→B=(0,1) The vectors A, B are linearly dependent if their determinant is zero. i.e.…

Q: 2.2.8 Show that if a matrix is positive definite then it is invertible, and its inverse is also…

A:

Q: Find the augmented matrices of th e linear systems x - y = 0 ,2x+y=3

A:

Q: (6) Consider the real symmetric matrix (2 1 0 A = 1 1 2 Construct an orthogonal matrix Q of eigen…

A:

Q: 0. LetA 8 l show that there are no 2 x 2 matrix B such that %3D B2 = A. %3D

A:

Q: Solve the initial value problem for the linear system a' = Ax in dimension 3, where %3D 7 -1 A= |1…

A:

Q: 3.0 4.5 7.0 2.5 9.0 0.5 f(x) 2.5 1.0 a) By using Quadratic Spline Method, determine the 8…

A: Given: The following data set: x 3.0 4.5 7.0 9.0 fx 2.5 1.0 2.5 0.5   To determine: The 8…

Q: Let A be an mxn matrix. Then, the homogeneous equation AX = 0 is consistent if and only if the…

A: Given :- Let A be an m×n matrix. Then, the homogeneous equation AX =O is consistent if and only if…

Q: Example:5 Verify Cayley-Hamilton theorem for the [5 matrix A= 31 and find its inverse. 2

A:

Q: 2 2 1 2 -1 2 is orthogonal. Verify whether the matrix A = 3. -1 2 2

A: Given matrix is, A=132212-12-122

Q: 2. Find a single matrix equal to [1 - i 1+0, where i = √-1 (imaginary unit).

A: To find the product of the given 3 matrices.

Q: 4. (a) Prove that if A is an n x n invertible matrix that satisfies the equation A2 = A then A is…

A: Given [A] is n×n invertible matrix.  And satisfies A2 = A a) To prove [A] is an identity matrix b)…

Q: Find a 2×2 matrix A for which E1 = span [1      and      E2 = span [2                     2]…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.