1) Consider the following matrix: 1 7 8 8 A = 1 3 3 -2 -5 1 -8 Answer the following questions: 1.1) Write A in row-echelon form R. 1.2) Find elementary matrices E, F and G such that A = EFGR.

Q: Consider the following matrix A-( ) %3D If the cigenvalues of matrix A are 4 and 8, then r = 5, y =8…

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Q: Consider the matrix 19 19 A = 19 10A° = 5XT + I2, When solving the matrix equation , the matrix X…

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Q: 30: If reflection about origin is represented by the matrix R reflect the letter %3D ro 4 4 1 1 01…

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Q: Given the matrix 2 2 3 1 2 A = 0 2 7 7 Find the |A| by transforming the matrix A to the triangular…

A: Given :A=222023771

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

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Q: Given the matrix 2 2 2 A = 0 2 3 7 7 1 Find the |A| by transforming the matrix A to the triangular…

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Q: Show that if A is a square matrix that satisfies the equation A2 -2A +I= 0, then A-1 = 2I -A.

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Q: Are there values of rand s for which 1 0 O r - 0 s- 4 r+6 7 has rank 1 or 2? If so, find those…

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Q: Show AB + BA for the indicated matrices. A= 2 3] B = -1

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Q: 1 6. Let A = 5 [; ] [:] 3 and B = 1 0 2 (a) Calculate the matrix Aª. (b) Calculate the matrix B-2.…

A: Use the properties of matrix and matrix multiplication to determine the value of each term. The…

Q: Consider A and B are two square matrices and B is a scalar. Calculate (BA^T B)^(-1) = *

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Q: 6. (a) Find the matrix A so that AB=C, where C1 C2 C3 b, b, bz 2 B= b, b2 b3 & C= C1 C2 C3) а, а аз…

A: AB=C

Q: Factor the matrix from the previous question into A = QAQ", where Q is an orthogonal matrix. [1 A =…

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Q: Let A = 1.8 -6 : J.c = , ].- [1 2 l4 5 6] [1 0 lo 1 [0] ol.C = 6 , and V = |1|. What is the sum of…

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Q: 5.1) Find the matrix A if det(A) =2 and the classical adjoint is -1 - 2 ad j(A) = - 6 1 6. 24 4.

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Q: Consider the matrices A = [₁, B = 3₁ C= ¹), D=1 K₁ = [5], K₂=[₁²2] Solve AX + BY = K₁ CX + DY = K₂…

A: Concept: We have the matrices A=3211 , B=0110 , C=111-1 , D=11-14 Now the matrices X and Y are…

Q: 9.1 (a) Write the following set of equations in matrix form: 40%3D 5х, + 2x, 10- x, = X3 4x, + 8x,…

A: We will find out the required values.

Q: - 2 Determine det D, adj D and D for the matrix D = 1 2 3 - 2 -1 -2 3

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Q: DEMONSTRATE THAT A A-1= A-1A = I      FOR THE MATRIX BELOW     1 -1 2 2 -3 4 1 0 3

A: Given matrix A=1-122-34103 We have to  prove that AA-1=A-1A=I We know that A-1=AdjAA

Q: Determine the cofactor of 2 in the matrix A = 1 9. 7 4 O-4 3. O -3 2.

A: Cofactor of any element aij is the determinant of the matrix formed by deleting row i and column j…

Q: Find the SVD of the matrix: 1 2 34 A = 0 0 0 0

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Q: b) If C is an orthogonal matrix and D = C + C-1 show that D is a symmetric matrix.

A: We have to show D is symmetric.

Q: Which of the following is the reduced row echelon form of the given matrix? 1 a b. a. A %3D a. b. b.…

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Q: Match the two matrices A, B with their product AB. i Instructions 1 0 2 6 7 4 3 4 5 -3 9 0 6 1 [1 -2…

A: Match the two matrices A, B with their product AB.

Q: Convert the following augmented matrix to reduced echelon form, with scalars in Z5. 0 3 1 3 2 1 4 1…

A: Row reduced echelon form of the Matrix

Q: 1 2 Compute the adjoint matrix of A 3 2 2 2 3 Select one: a. -7 4 -5 7 -7 -5 3 -1 -2 %3D -7 -5 41 d.…

A: We have given a matrix and we have to find the adjoint of A.

Q: a) Consider the matrices A and B: 4 -3 A =-2 7 1 8 6. -5 B = -3 -2 Which element is in row 2, column…

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Q: Illustrate the Gersgorin theorem by the matrix 2 1+ 2i 0 A = -1 -2 – 2i 1/4 1/41/2 140 12 1/7 1/2…

A: We state the theorem and explain it with the help of the given matrix A.

Q: Identify a matrix P that diagonalizes 2 6 A = a. 1 P = - 2 Ob. P = -1 0 0 2 Oc. P = 01 1 2 O d. -2 P…

A: Solution

Q: Find a matrix B such that AB = I, where [ ] 8 1 1 0 A = and I = -8 8 0 1 1 a b Hint: Let B = %3D c d…

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Q: Consider the following matrix: -31 A = -3 -4 9. 1 -2 (a) Verify that A is diagonalizable. (b) Find…

A: Since it is multiple questions with multipart, as per our company guidelines we have to solve the…

Q: 1 1 1 A =1 1 1 1 2 1 . How many nonzero elements are there in the adjoint matrix of matrix A?

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Q: 3.3. Let a matrix B is B = [, В -2 3 Find B6 by using a nonsingular matrix P such that D = P¯'BP is…

A: B=01-23 Characteristic equation of B is given by  λ2-trBλ+detB=0 where trB, detBdenotes the trace…

Q: Give a 3 x 3 elementary matrix E which will carry out the row operation R + Ry. E = Test that E…

A: The elementary matrix E with the raw operation R1↔R3 is: E=001010100 Because it the matrix obtained…

Q: Consider the matrix A = Calculate a22 = 8 5 d n -( :-(29 766 b f 468 h с Calculate 932 = a e

A: It is provided that: A=852766468·dngbfahce. We need to calculate a22, a32.

Q: Given the matrix 2 22 A = 0 2 3 7 7 1 Find the |A| by transforming the matrix A to the triangular…

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Q: Let A be the following matrix 7 7 7 0 3 0 7 Then for which column vector b, the equation Ax = b has…

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Q: I. State whether or not the given matrix is (a) upper triangular, (b) lower triangular, (c)…

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Q: Find the minor M12 and cofactor A12 of matrix A. 1 6 A = 3 3 -2 0 1 8.

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Q: Given the matrix 6 0 0 A= 0 2 2 0 2 2 find an orthogonal diagonalization of A: A = QDQ"

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Q: Enter a 3 x 3 symmetric matrix A that has entries a11 = 1, a22 = 5, a33 = 4, a12 = 3, a13 = 2, and =…

A: Given A is 3×3 Symmetric matrix with entries a11=1 , a22=5 , a33=4 , a12=3a13=2 and a32=0.We know…

Q: Given the matrix [1 2 1 A = 2 3 −1 3 5 0 01 Determine if the matrix equation Ax=b has a solution for…

A: We use properties of solution to system of linear equation.

Q: 7. ). Find all a and 3 > 0 so that the matrix B : 23 6 2 is %3D В 2 diagonally dominant; 12G

A: For a matrix is to be diagonally dominant, there are three conditions or properties, first one is…

Q: Find all a and B >0 so that the matrix B = 23 6 2 is diagonally dominant;

A: A square matrix is diagonally dominant if   for .

Q: Given the matrix 2 2 2 3 1 A = 0 2 7 7 Find the |A| by transforming the matrix A to the triangular…

A: Given :A=222023771

Q: C be the matrix defined as a₁ an C = a-1 9₂ az az a a₂ a, a az a4 1 A an an-l an-2 a₁

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Q: 1 4 [5 0 lo 4 -3] b) Given D = -2 3 1 -2 1 85 72 -54] A =| 50 32 -24. -35 -24 18 Find a matrix BT ,…

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Q: 8 6. Let A -4 -2 Find two different diagonal matrices D and the corresponding matrix S such that A…

A: Given:    2x2 Matrix is given

Q: Find all a and B> 0 so that the matrix 4 a 28 5 4 2 is strictly diagonally dominant.

A: In a diagonally dominant square matrix, the magnitude of the element corresponding to the diagonal,…

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.