2. Let Gaussian elimination without pivoting be applied to a symmetric positive definite matrix A, Write A, the matrix obtained after the first step, as an 4(1) -(% 0 a11 a12 B(n-1)(n-1) a) Show that B-1)(n-1) = (b) is symmetric and positive definite. b) If a ≤1, then b≤1.

Q: 1. Let, A = -1 21 Find the matrix -5A3 + 2A? + 4A + 512. 9 21

A: Given: A=-1292 Determine A3. A3=-1292-1292-1292=192922-1292=-14218962

Q: B= 2 Compute each matrix sum or product if it is defined. If an expression is undefined, explain…

A: For solving the given problem:

Q: Let - (; ;) 5 3 A = 2 1 a) Calculate A-1 by any method. b) Using your answer to part (a), explicitly…

A:

Q: Verify that if r < s, then rows rand s of a matrix can be interchanged by performing 2(s - r) - 1…

A:

Q: the given matrix B, =[3 B Show that the matrix B is diagonalizable [Cite any theorems used] Find…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: 1 Find a matrix P that satisfies P 1 9 1 2 0 3 0 900 23 1 7 1 1

A: We have to find the matrix P that satisfies the given equation.

Q: 17- Let A be 5 x 5 matrix and det(4) = 2. What is the value of der(24)? a) 128 b) 32 16 64 LEave…

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Q: 2 7 Which of the following is the matrix C that satisfies the equality (c" +312) 1 4 -1 3 (a) 2 -5…

A: We have to find matrix

Q: 04) X = [ Y = ; Hand Z = [ 3 Q.4) X Prove the Distributive laws of multiplication over Subtraction…

A: The given matrices are X=23-10,Y=0131  and  Z=22-10. The distributive law of multiplication over…

Q: -1 2 4 Find the 1-norm of the matrix 3 -2 0 1 -1 2.

A:

Q: 1 31 A = 2 7 . A·B = B · A = I3×3 -2 -4 -5. ]

A:

Q: Q9. As usual, let In denote the n x n identity matrix. 1 - (a) Find a 2 × 2 matrix such that A² =…

A:

Q: 2. a) Let A = answer. [2]. Find the matrices A² and A³. What can be the matrix A"? Justify your -11

A:

Q: (1) If a matrix A has 10 columns with nullity(A) = 5 and nullity(A) - 3, then A has 7 rows? (i) If A…

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Q: 1) USE THE INVERSE OF THE COEFFICIENT MATRIX, S.N=0 4 -1 Last digit of S.N.] A = 1 1 b = 4 1 6 0 -2

A: Given A=4-1Last digit of S.N11-5-216  b=140

Q: Q4: If the matrix A = (; :),s Show that A2- 2A – 21 = 0.

A: We observe that characteristics eqn of A will be x^2-2x-2=0. By Caley hamilton tum put x=A we get,…

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: For each 2 x 2 real matrix A find the canonical form B and an invertible matrix P such that P-1AP =…

A:

Q: 1 8 Which of the entries in the matrix 2 -3 -7 9 A) 4 B) 1 Ⓒ-3 (D) -6 -61 4 has-37 as its cofactor?…

A: We have to find correct option by finding element whose cofactor is -37

Q: Let A =mnd B- then the matrix (2AB + A")" is equal to O None of these O equal to the above 2 17

A:

Q: Which of the following is the matrix C that satisfies the equality (CT +312) -1 3 (a) 2 -5 (:) 5 -2…

A: First take inverse on both sides of matrix equation CT+3I2-1=2714. CT+3I2-1=2714CT+3I2-1-1=2714-1…

Q: 2 Be A, a square matrix i. Given that A holds = 44 + 5I . Prove that A is reversible, and express A-…

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Q: Q2) Find x for the following matrix 3 1 x| a) -1 3 4= -30 1 ol 1 |1 2 1| b) 12 x 2=0 13 6 xl

A: We need to solve the determinant and find the value of x.  Now, if we have a 3×3 matrix…

Q: Suppose that 2 3 Solve the linear system Ax = b for each of the following matrices b: 8 (b) 15 (a)

A: Given: A-1=1213 (a) Ax=bx=A-1b Substitute the respective values. x=121346=4+124+18=1622 Therefore,…

Q: Determine all values of a and b such that (the first line correspond to the first row of each matrix…

A: This is a problem related to matrix operation Based on the general formula and concept we will…

Q: Now write ageneric exampledaux2 motrix a with entries paying close attention to the subscripts है…

A: Generic Example of a 4×2 matrix  Let A be a 4×2  matrix. For any entry,aij i represents the ith row,…