if (A|b) is in reduced row echelon form, prove that A is also in reduced row echelon form.

Q: Use Cramer's rule to compute the solution of the system. X1 + X2 = 5 AX1 + 4x3 = 0 X2 4x3 = 6 %3D x1…

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Q: Find the matrix of the quadratic form 2x,² + 3x2² – x3² – 4x1x2 +2 x1X3 + 6x2X3

A: The symmetric matrix for quadratic form ax12+bx22+cx32+dx1x2+ex2x3+fx1x3 can be written as…

Q: If A = (ajj) is the matrix of the quadratic form x + 2x, + 2x? + 6x1x2 – 22x1x3 - 8x2x3, then the…

A: If A=aij is the matrix of the quadratic form x12+2x22+2x32+6x1x2-22x1x3-8x2x3, then we have to find…

Q: Explain the dimension of the row space.

A: The dimension of the row space is called the rank of the matrix. This is the same as the maximum…

Q: 2) Is there a choice of rational numbers a, b, c, d for which the linear system has no

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

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: do the column space and the row space always have the same dimension

A: Let's say matrix A is m x n. A has n columns, each of which are m-dimensional vectors. Let's say the…

Q: Use Cramer's rule to compute the solution of the system. 4x, + 3x2 + 4x3 = 8 4x1 X3 = 2 + - 2x1 +…

A: As given by the question There are given that the system of equation:…

Q: Use the Gauss-Jordan reduction to solve the following linear system: 5x3 6x3 4x2 3x1 -30 | 28x3 2x1

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Q: Find the matrix of the quadratic form. Assume x is in R2. a. 1x21 – 4x1x2 + 5x22 b. 3x21 + 2x1x2

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Q: Every row operation is reversible. O True O False

A: Every row operation is reversible.

Q: Use Cramer's rule to determine how many solutions the following system of equations has. -4x +2y +…

A: Use Cramer's Rule

Q: O Grven A- 131 find beses Aor rowĄ, coLA and null A.

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Q: If U is the reduced row echelon form of A, then A and U have the same row spaces, Select one: True…

A: The solution is given below

Q: Matrix A is 2 x 7 and matrix B is 2

A: Given, Matrix A is 2 x 7 and matrix B is 2 x 8.

Q: Use the Gauss-Jordan reduction to solve the following linear system: х2 2x3 -1 5x1 4x2 Зх3 -4 2x1…

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Q: Use Cramer's rule to solve the following linear system: X1 – 3x2 + x3 = 4 2x1 – x2 = -2 4.x1 – 3x3 =…

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Q: b) Use row reduction to show 1 1 1 b с| %3 (b — а)(с — а)(с — b). а la' z² b2 c2

A: given,                 we have to proof L.H.S = R.H.S

Q: Which one of the followings is reduced row echelon form?

A: Reduced Row Echelon Form A matrix is in row echelon form  when it satisfies the following…

Q: Find the matrix of the quadratic form. Assume x is in R2. a. 5 x12+ 16x1x2 – 5x22 b. 2x1x2

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Q: Show that if A is skew symmetric, then the elements on the main diagonal of A are all zero.

A: given that A is skew symmetric

Q: Which of the following is not in reduced row echelon form?

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Q: Show that the elementary row operations

A: To prove that the elementary  row operations               Ei+λEj⇒Ei           and           Ei⇔Ej

Q: in finding the inverse A1, use the given row operations to find the equivalent of

A: The given matrix is A=1-122063-57,in finding the inverse A-1 using the row operation to find the…

Q: Apply Gauss Elimination method to triangularize the following set of quadratic equations. X1 + 4x2 –…

A: The given equations are  x1 + 4x2 - x3 = - 5 x1 + x2 - 6x3 = - 12 3x1 - x2 - x3 = 4 In the matrix…

Q: Solve it correctlys

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Q: If U is the reduced row echelon form of A, then A and U have the same row spaces. Select one: True…

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Q: Use row operations to change the matrix to reduced form. 111 16 3 4 8 29

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Q: form the row operation R, and replace R, on the

A: Given,  6000200024255 The row operation is performed.

Q: Use the Gauss-Jordan reduction to solve the following linear system: 3x3 -6 L2 + 6x1 5x2 + 4x3 -3 -…

A: Introduction: When an augmented matrix can be reduced completely in its row-reduced echelon form,…

Q: Investigate the stability of the following system (Consider the quadratic form as lya punor system.)…

A: For any queries please let me know through comments. I will try to reply ASAP! Please like if…

Q: Use row reduction to show 1 1 b 3 (b — а)(с — а)(с - b). a la² b² c2l

A: Question:-

Q: 1 -2 3 -2 1 2 -4 -2 4. 4,

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Q: / Find a Row A, CoL A, Null (A), whore. A= bazis and dimension Lor 2. 1- -31 -2

A: we have to solve given problem:

Q: Find the maximum number of linearly independent rows in the following matrix r0 1 -3 -1] 0 0 1 3 1…

A: Given matrix is: Z=01-3-10011310211-20 R1↔R3⇒3102001101-3111-20 R1→R13⇒113023001101-3-111-20

Q: Find a basis for the solution space of the following linear system + 3x2 + 4x3 + 5x4 201 + 6x2 + 9x3…

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

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Q: Use Gauss-Jordan Elimination to find the inverse of -1 4 2 2 4 2 0 2

A: Given is the matrix  -142   324   202 In Gauss Jordan-method the inverse of the matrix is found by…

Q: Use Cramer's rule to compute the solution of the system. 4x1 + 2x2 = 8 3x, + 7x2 = 17

A: We will find the solution using Cramer's rule as following.

Q: Use row operations to change the matrix to reduced form. 10 - 3 1 0 1 6 0 0 2 6 10 - 3 1 0 1 6 0 0 2…

A: Given:          10-3   1016   0002-6   Reduced row echelon form        R3←R3÷2          =10-3   1016…

Q: For Exercise, perform the elementary row operations on 4 2 6. - 3 6 -R2 →R2

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Q: Use row reduction to find the v * + 2y + z = 1 * + 3y + 2z = 4 3x + 7y + 42z = u

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Q: Find the matrix of the quadratic form 2x12 + 3x22 – x3² + 4x1x2 – 2 x1X3 + 6x2x3

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Q: Use Gauss-Jordan Elimination to find the inverse of -1 4 2 3 2 4 2 0 2

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Q: Use row operations to change the matrix to reduced form. 111 13 45 8 32 111 13 4 5 8 32

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Q: Prove that a linear system Ax = b is consistent if and only if the rank of (A | b) equals the rank…

A: Assume, Ax = b is consistent. Then in the column space of A lies B. Therefore, the dimension of the…

Q: Determine if the Columns of the matoisc b0rm a Justify each linearly independent Set. answer -3 3.…

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Q: Show that the following linear system is a strictly diagonally dominant: 7x1 – x 2 = 9 -X1 +7x2 – X3…

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Q: 6. Indicate all possible reduced row-echelon forms of be (a) def bed e fgh i jkl (b) mnpq

A: Given : A=abcdefghijklmnpq To find : reduced row-echelon forms of matrix A Pre-requisite :  Reduced…