1. Please find the rank of the matrix given below. If any, please also find the inverse of the matrix 0. 1 A = 1 1 2 14 16,

Q: 7. Given the following augmented matrix, list all the variables {x1, ... , X5}. Indicate which are…

A: We find free variables by using given augmented matrix.

Q: 2- For any constant matrix A, if A² = 0 then a- e4' =I +At b- e4 =I - A12 c- e At-A²1 ² The correct…

A:

Q: (iv). Find det(A¯1) of the following matrix: 1 3 -1 2 1

A:

Q: Let [1 2 [1 A = 2 41 1 3 and B = |2 1 [2 2 6] 2 4] 3 [1 2] Find the elementary matrix, E such that…

A: Two matrices A=124213102 and B=124213226 are given. We have to calculate the matrix E that satisfies…

Q: 5. Find the rank and also the numerical rank of the matrix 1 1 .000a 0.000a where a is the last…

A: To find the rank and numerical of the matrix: 11.0007000.0007

Q: Linear algebra problem

A:

Q: Example 4.16. Using House-holder's method, reduce the following matrix to the tri- 1 diagonal form:…

A: First check  about the symmetricity (A square matrix  A is called symmetric if A=AT) AT=143412321…

Q: Apply the Gauss-Jordan method to invert the matrix given below. 1 0 0 01 1 1 2 1 1 Write down each…

A:

Q: [1 2 0] 3. If is A =3 4 0 create a matrix B whose entries are three times the difference of an…

A: Since I have solved similar ones, Let us find the matrix B and and it's determinant using built in…

Q: 4. Use the following matrices and find an elementary matrix E that satisfies the stated equation 13…

A:

Q: Question 28) Determine whether the given matrix is elementary. (a) (b) (c) (d) 외 1 0 -5 1 -5 1 10 1…

A:

Q: Question2 Find the Rank and Nullity of the matrix -1 20 4 5 3 -7 2 1 4 A= 2 -5 2 4 6. 1 4 -9 2 -4 -4…

A:

Q: A is a 3 x 3 matrix, det(A) = -2. What is the value of det(3A)? %3D -6 O 54 O -54 O 6 O 27

A: Given :-  A is a 3×3 matrix , det A =-2. To Determine :-  The value of det 3A.

Q: One of the following is not an elementary matrix 100 a) 010 b) 0 60 00 1 00 1 [100 00 1 c) 01 2 d)…

A:

Q: 1.6.1(b,c) Is given matrix diagonalizable? If so, what are the corresponding matrices P and D? 1 1 0…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Question 1 Find an LU factorization of the matrix A 3 5 5 20 6 31 A = -2 -1 -1 4 -1 7 1 7 1. 1.

A: Find an LU factorization of the matrix A

Q: *8. Suppose A is a square matrix satisfving the equation A3 – 3A +I = 0. Show that A

A: We have to solve given problem:

Q: 1 2 3 A =2 2 8 10 3 3 10 13

A:

Q: One of the following is not an elementary matrix 100 100 a) 0 0 1 b) 0-50 020 0 0 1 104 00 1 010 d)…

A:

Q: Find the inverse of the given matrix if the matrix is invertible 3 4 -1 1 0 2 5 -4 [1 0 1' 0 1 1 1 1…

A:

Q: 4. Find A-1 for the following Matrix [1 3] (a) A = 3 7 [2 5 (b) А — 7 17 [3 (c) A = 4 12 19

A:

Q: (5 4 1) 1. For the matrix A= 0 0 3, state 9 8 6

A:

Q: [1 1 1] L3 -2 3 1[k [k 1 1 -2||1 = 14 1

A: Given,           k11·10301-23-21·k11=14To find : The value of k that satisfies the following matrix…

Q: - E- is multiplied by is equal to zero, then matrix If matrix A 3 B1 C.o D-2

A:

Q: c -r and det(A) = 6, which of the following could represent A d -t . Given matrix A =

A: Consider a matrix A. The inverse of the matrix is defined as, A-1=1AAdjA A defines the determinant…

Q: Which of the following matrices is not in Reduced Row Echelon Form? [1 0 4 31 [1 0 4 01 0 1 5 2 0 1…

A:

Q: 1) Find the reduced echelon form of each matrix using Gauss-Jordan reduction 4 15 29 2 45 15 1 2 3 9…

A: We have to solve given problems;

Q: Example 4.15. Using Given's method, reduce the following matrix to the tri-diagonal 2 1 3 form: A =…

A: Step 2 contains the required form of the matrix.

Q: -1 If A= BD and 2A + B + X = 0 then the matrix X is O a. 1 - 2 10 3 Ob. 1 7 13 С. 3 2 1 d. 1 2 - 7 –…

A: ans: Given A=2-4-6-8, B=3-215⇒2A+B+X=0⇒X=-2A-B⇒X=-21234-3-215

Q: Find the rank of the following matrix. rank(A)- Question 8 grade: 0 1 2 1 1] 1 2 1 1 1 2 1 0 1 1 2…

A:

Q: 1. Find an LU factorization of the matrix A 5 [2 A = [4 L4 3 9. -3 24]

A: In Linear algebra, lower–upper decomposition or factorization factors a matrix as the product of a…

Q: [4 2 If A is a non-singular matrix whose inverse is |1 1 find A. * 司 1. 1 -2 B. -1] -1] 1 1/2 C.…

A:

Q: 11 is equal to 23 The inverse of the matrix A O A. 3 -1 -2 1 OB. -13 1 -2 C. -2 3 -1 1 D. None of…

A: inverse=?

Q: Question 1 Determine the dimension of Null A and Col A for the matrix [-3 6 -1 1 -7] -2 2 3 -1 -4 5…

A:

Q: 15. If A=| B = 0 1 and C = |1 0 then find the matrix (Av B) 0 c

A:

Q: 2. Find the rank of the matrix 1 3 4 5 8 9. 10 11 12 13 14 15 16

A:

Q: If A is n x n matrix, invertible, and B is n × n. Then Col(BA) =Col(B) O True O False

A:

Q: One of the following is not an elementary matrix 100 100 a) 010 b) 060 00 1 001 100 001 c) 012 d)…

A:

Q: Question 3 2 3 11 Which is the matrix inverse to the matrix 3 2 1 10 1

A: We have to find inverse

Q: Find the inverse of the matrix (if it exists). (Round your answers to four decimal places. If an…

A: Given that, the matrix is A=0.20-0.40.9-10.710-0.3. It is known that, the formula for the inverse of…

Q: The matrix is defined as A=(²₁ 2¹) has characteristic equation of 2² + DA + 3, so the value of D is.…

A:

Q: 4 2 If A is a non-singular matrix whose inverse is 1 1 find A. - 2 -1 1 D. -1 1/2 1 В. С. -1/2 2 А.…

A: Goal is to find inverse of matrix 4211

Q: 4. Find the inverse matrix of A (A-1) 3 1 10 A= 2 5 4 -1 -3 1

A:

Q: 1 2 1 Let A=0 10 be a matrix and det(A)30, then the value of k is 5 3 k 1. 10 5,

A:

Q: 13. Reduce the following matrix to reduced echelon form and find its rank. 1 2 2 -1 -1 -5 1 2 3 4 -2…

A: According to question, Given matrix, 122-1-1-51234-2-3

Q: Consider the production model x = Cx+d for an economy with two sectors, where C = The inverse matrix…

A: Given production model is x=Cx+d = 0.00.50.60.5x+4050   To Find: Inverse matrix x

Q: One of the following is not an elementary matrix 100 100 a) 00 1 b) 0 -5 0 020 0 0 1 104 001 c) 010…

A:

Q: Find the reduced echelon form of this augmented matrix 10 0 250 1 1 0 100 1 1 400

A: The first non-zero number in the first row (the leading entry) is the number 1. The second row also…

Q: 1 2 2 2 e M2,2: Question 1. Are matrices a) Linearly independent?

A: We will check whether the given matrices are linearly independent or not.

Q: If A is a 4x4 order matrix and det(A) = -1, then the value of det(3A) is Select one: O a. -81 O b.…

A: we are allow to solve one question at a time thank you

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.