O Consider fhe matrix-valved fuctious ACx) = X2 x 3x B(X)=|x-1 2x Vx eR a) Evaluate and simplrhy the fundion G (x) = 2 ACQx+i)- B&-2), VxelR O Solve with vesped to Yos the madrix equation 3Ax) + 2 (YGx)'+ A(W) = A(xti) - B) %3D

Q: a) Prove the following: a+b a a a+b =b° (3a +b) a a a a+b

A: Since you have posted more than one question, we solve the first one for you. For the other…

Q: if matrix A is ] and matrix B is will have same result matrix. • (AB)T # B'AT 1 Add file if matrix A…

A:

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: B) Suppose A is an invertible matrix inM, (R). And x, y E R". Prove it: det(A+ ry") = (1+y"…

A: Given: A is an invertible matrix in Mn(ℝ) x,y∈ℝn To prove: det(A+xyT)=(I+yTA-1x)det(A)

Q: (f) q = -ư² + 4uv – 6uw – 4v2 – 7w?

A:

Q: rewrite ax^2+by^2+cz^2+dxy+exz+fyz+gx+hy+iz+j=0 in  standard form by matrix

A: The objective of the question is to rewrite the given quadratic equation in three variables in…

Q: Given matrix A = [ 4 3 3                                 3 4 3                                 3 3…

A: Given matrix is, A=433343334 The objective is to find the determinant A290+I-1 Now, the determinant…

Q: For matrix A and a scalar k, (kA)T is equal to: k(A^T) k(A) (k^2) x (A) (k^2) x (A^T)

A: We will solve the matrix operation.

Q: a) Use Excel Plot the function f(x)=2x-1.75x² +1.1x³ -0.25x* for x from -2 to 3 at a step size of…

A: As per the question we are given the function : f(x) = 2x - 1.75x2 + 1.1x3 - 0.25x4 And we have to…

Q: Prove or disprove by giving a counter example. If b∈R^n ,then Ax=b has a solution in x for any…

A: This statement is false.

Q: 2. A = 77₁b = 3 25 -1 3

A: Given, .If A=, than .

Q: 13. A and B are two square matrices of the same dimension. We are given that Aw = 5w and Bw=3w.…

A:

Q: Find a 2 x 2 matrix C such that C^-1 does not exist. C = 0 (C can not equal the zero matrix), and C…

A:

Q: Suppose that Q is 3 x 2 matrix with orthonormal columns then Oa Q'Q +1 Ob QQ" - I OcQ" - Q Od. Q"Q-…

A: The detailed solution along with the final answer is described below.

Q: If all the entries of a matrix A are integers and det (A) = 1 then the entries of A^− 1 (the…

A:

Q: Solve the matrix equation AX = B, where -1 하 A: 1 and B 1 1 [6] 0 1 =

A:

Q: 8. For the column matrix v=(v₁) we have explain then: (VA); =Vkaki

A:

Q: 1 2 3 1[1 1 07 M = 20 0 1 3|1 0 0

A: Write the relation M as a set of ordered pairs. If x,y is an ordered pair in M , then (y,x) is and…

Q: For this matrix A, find a diagonal matrix D and invertible matrix P with inverse P such that A = P D…

A:

Q: Find A of the matrix 1- A = 2. -4 2. 1.

A: The inverse of the matrix A of order n is defined as a matrix B of order n such that AB=BA=I, where…

Q: Given the matrix      A=       [4 -1   0   2] , then the trace of A^3 is?

A:

Q: solve for x and y in the matrix A= [ x -4 3 y] if A^2 = [52 -36  27  -11] x = y =

A:

Q: I need help with this initial value problem using matrices: x1'= 4x1-3x2 x2'= 8x1-6x2 Initial…

A:

Q: Bis a 4 x 3 matrix. the solutions to the equation are given by S and t x = 35+ 25,4 ary real…

A:

Q: The following matrix product is used in discussing two thin lenses in air: (1 -1/f2 M where fi and…

A:

Q: Suppose A, B, and X are n x n matricies with A, X, and A - AX invertible and suppose (A - AX)^-1 =…

A:

Q: Let A be 3x5 matrix. Then AX=b has always infinitly many solutions.

A: Since not a particular question asked ,as per guidelines solution to first question is given below

Q: The equilibrium point of æ' = Ax + b is xo =-A¯'b for any matrix A. O True O False

A:

Q: 5) Find dx/dt of Matrix: X 5e-1 2e-¹ -7e-t

A: We know , d/dx(e-t) = -e-t   Given X = 5e-t2e-t-7e-t

Q: Apply the conjugate gradient method to solve Ax = b = ones(lOO, 1), where A is the -1, 2, -1 second…

A: As per the question we have to implement the MATLAB Code for the conjugate gradient method in order…

Q: [1 2) 13 · X = 2-

A:

Q: In Exercises 19-20, find TÂ(x), and express your answer in matrix form. 1 2 ^= 3x-[-] ; X= 4 19. (a)…

A:

Q: Let A = [0 1 0 0 ], A^(-1) is equal to: * Does not exist Identity matrix Null matrix

A:

Q: ^ = [1 ] A If A is diagonalizable, find an invertible 2 x 2 matrix P and a 2 x 2 diagonal matrix D…

A: Given that the matrix A=0-440. If the given matrix is diagonalizable , find an invertible matrix and…

Q: 8. Solve the matrix equation Ax = b where A 1 0 and b %3D -4

A: The given matrix equation is - A = 121130-1-41 and b = 11-1 Converting the given matrix equation…

Q: if the chractrestic polynomial of a matrix A is p(^) = (^ +1)(^ - 2)2 then det(-A) +tr (A) = 1 7 -2…

A: As we have 3 roots of characteristics polynomial.

Q: By using the Cayley-Hamilton Theorem, find e^(At) of the following matrix A = [1 2;-2 -3].

A: Given information Matrix :- A=12-2-3 Find eAt using Cayley-Hamilton Theorem.

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.