(c) 0 is neither diagonalizable nor

Q: a) Find the matrix of the quadratic form. Assume x is in R3 5x3-x3 +7x3-5x1x2 -3x1x3

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Q: -2 is diagonalizable. Show that B 2. Select one: 6 0 O A( 0. O B. None of the Above 6 0 1. 6. D. 0.…

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Q: Consider the fourth-degree polynomial equation a₁ + b₁x²q₁x² + b₂ a₂+ b₂x² a₂x² + b₂ a3 + b3x² a3x²…

A: Given that We know that determinant of a matrix is equal to zero if any two rows or two columns are…

Q: 2.x - y-z = 0 5x - 2у +2: 3 Зх + у - 2: -8

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Q: What does interchanging any two rows (or columns) do to the value of the determinant?

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Q: Find two examples to demonstrate that if (a-d)2+4bc =0 then A may or may be diagonalizable

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Q: 6. Find the matrix of the quadratic form. Assume x is in R³. a. 3x} – 2x3 + 5.x + 4x1x2 – 6x1X3 b.…

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Q: Explain why the determinant of a square matrix A is the same as the determinant of the transpose of…

A: Explanation

Q: Express the linear function as F(x) = CX for some matrix C. f(x1,x2,x3,x4) = (5x3 - x1, 2x3 + x4,…

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Q: Solve the following set of simultaneous equations using Cramer's rule: X1 + X2 + X3 = 6 X1 – X2 + X3…

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Q: X1 3x2 + 5x3 + 15x4 T(x) = |3x₁ + 8x2 − 2x3 − 23x4 4x17x2 + x3 - 16x4

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Q: 3.- Prove the following statement: If the vectors c and d are solutions of the homogeneous linear…

A: Given the statement,If the vectors  and  are solutions of the homogeneous linear system , then  is…

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Q: Let A 1 2 −1 -2 3 -2 -1 1 1 Diagonalize A to find A100.

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Q: a 12 Let A 0 a 1 For what value of a is A diagonalizable? Explain your 00 a answer.

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Q: Show that the inverse of a nonsingular lower triangular matrix is lower triangular.

A: We have to prove that inverse of a nonsingular lower triangular matrix is lower triangular.

Q: Exercise 51. Is there a square matrix X with real entries such that det(X¹X) = -3?

A: detXTX=-3 X is a square matrix with real entries.

Q: Explain why v = ( 1, 0, -1) cannot be a row of A and also in the nullspace.

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Q: [121] In other words, write A = SDS-¹ = SDSt where D is a diagonal matrix and S is an isome- try.…

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Q: BV St P X, X2 X3 S, 8 2 2 10 Const. 32 30 40 2 8. -5-3-2

A: Given the following tableau: BV P X1 X2 X3 S1 S2 S3 const S1 0 8  2  2 1 0 0 32 S2 0 10 6 4 0…

Q: Let a and b be integers. (a) Show that b is a linear combination of a + 3b and a + 2b. (b) Show that…

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Q: Find the solution of the linear system using the Cramer rule 7x1 – 2x2 – 3x3 = -3 X1 + 5x2 + x3 = 14…

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Q: For the​ matrixA=daig(-2,-1,2), put the following values in increasing​ order: det(A),​ rank(A),…

A: Given the matrix A=daig(-2,-1,2) is diagonal matrix Therefore the eigen values of A are -2, -1, 2.

Q: Find the matrix of the reflection about the line L.

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Q: [1 |A = [a1, a2, a3, a4] 2 11 5 0 3 -1 4 0

A: According to the given information, it is required to find a linear dependence between the columns…

Q: Do NOT row reduce! (a) Write the augmented matrix whose row reduction would find [x]B . (b) Write…

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Q: Determine whether or not A = 25 is diagonalizable. Justify your answer. 1

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Q: stitution? I have to use the Column Correspon

A: Is (1,2,3,4,5,6)∈ span( (1,1,1,1,1,1),(0,1,0,1,0,2),(6,5,4,3,2,1)) > A x1 x2 x3 x4 x5 x6…

Q: Enter the numbers that correspond to elementary matrices from this list. For example, if just the…

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Q: If X and Y are two full column-rank matrices of rank p, find all matrices A for which R(A) = R(X)…

A: Here given that are two column rank matrices of rank  so that where .Obviously  .From above…

Q: Describe the solution set, x= x₂ of x₁ + 4x2 - 7x3 = -6 in parametric vector form. Select the…

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Q: Consider the quadratic polynomial q(x) = 2x + 8x1x2 – 8x – 3x1 – 3x2 + 3. - - Find the symmetric…

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Q: Diagonalized  if possible, where is A=[■(4&0&1@1&1&0@3&0&1)].

A: Given A =   4 0 1     1 1 0     3 0 1

Q: Give the matrix representing the relation in the previous problem. Label the rows and columns.

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Q: I! the columns ola7*7 matnix D what Can be said abaut linearly independent , the solutions of DX = b…

A: Let D is a 7 x 7 matrix whose column are linearly independent. Since all columns are linearly…