Express the quadratic equation 2x2 + 4xy + 7x – 2y + 8 = 0, in the matrix form x" Ax + Kx + ƒ = 0, where xT Ax is the associated quadratic form and K is an appropriate matrix. ? ? A = ? ? K = ( ? ? ) f =

Q: Find a 2x2 matrix X that satisfies the matrix equation 45 X + 4 6 3 4 X. 1 2 23 x-[] -3 3 X= -1 3 A…

A: Given- 4545x+1023=3412x To Find- 2×2 matrix x such that it satisfies the above condition.

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: Find the characteristic equation of the matrix: 4 C = 2 -2 2.

A: Characteristic equation of the matrix C is given by  det ( C - λI ) = 0

Q: Find the singular values of the given matrix.

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Q: Find the matrix A of the quadratic form associated with the equation. 3x2 – 2xy + 3y2+ 8z2 – 27 = 0…

A: Answer

Q: Find the matrix A of the quadratic form associated with the equation.x2 + y2 − 4 = 0

A:

Q: 2. (a) Express -2+t+t +r' as a linear combination of 1-t, 1+r, and 1+1- or show that it cannot be…

A: We have to write in the linear combination.

Q: Determine the cofactor of a13 in the matrix. 2 -4 A =5 4 4 -4

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Q: 4. Find the symmetric matrix, diagonal form of the quadratic form Q = 2x? + 2y2 + 2z2 – 2xy – 2xz –…

A: Step:-1 Given quadratic form is  Q=2x2 +2y2 +2z2 -2xy -2xz -2yz Q=xyz 2-1-1-12-1-1-12 xyzQ=XTAXHere,…

Q: Find the symmetric matrix A associated with the given quadratic form. 2x2-3y2-z2-4xy

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Q: Find the symmetric matrix A associated with the given quadratic form.

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Q: 5 -1 5 1 6. -1 6 2

A:

Q: Find the singular values of the given matrix.

A: Given; Matrix A To find: Singular Values of A  Procedure: Calculate eigenvalues of ATA. The…

Q: Compute the quadratic form x¹Ax for the given matrix A and vector x. [59 0] A = 91 4, X = X2 04-2 x3…

A:

Q: Let be A, B, C,x. 5x5 matrixes such that A, B and C can be inverted such that AXB" – 151, = c-1…

A:

Q: 11. If a and B are the roots of the quadratic 3.x2 - 4x +6 = 0, find the value of (+) -3 12. For…

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Q: 4. Find the symmetric matrix, diagonal form of the quadratic form Q = 2x? + 2y2 + 2z2 - 2xy- 2xz -…

A: The objective is to find the symmetric matrix and diagonal form of the quadratic form…

Q: Find the matrix of the quadratic form associated with the equation. 12x2 - 4xy + 26y² - 56 = 0 I3D

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Q: 8. Given Matrix A, determine A-1 using cofactor |1 2 A =|-1 4 3 1. -2 VERSIT

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Q: A = 2 - 4 4 -2 6-9 7 -3 -1 -10 18 -7

A: Sol

Q: Find the singular values of the given matrix.

A: Given matrix

Q: m below using LL + = fr+ x+ 4.x, – 2x, = 4 9 = 'xp-+ x7+ of the matrix in a

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Q: 2 3 Show that the matrix A is singular. 4 6

A: Concept used: Singular matrix are the matrix that is not invertible. In other words the determinant…

Q: Suppose CA = I, (the nxn identity matrix). Show that the equation Ax = 0 has only the trivial…

A: Let A be m×n matrix then Rank(A) + Nullity(A) = number of columns of A Where Rank(A) is the…

Q: Express the quadratic equation 2x2 + 4xy + 7x – 2y + 8 = 0, in the matrix form x" Ax + Kx +f = 0,…

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Q: 2) Find the rank of the matrix A = 2 3 -1 ー1 1- ー2 -4 3. 3 -2 3. By deducing imto Echelon form.

A:

Q: 4 Solve the matrix equation 2X+A=B for X if A= -1 1and B= 2 . X= (Sinpily yr enswi

A: Given: A=-3-4-11-25 & B=1-21-3-4-9 Consider 2x+A=B Since the dimension of the given matrix, A…

Q: 2. Solve for x and y in the matrix equation below: x-y 4 2 [10 3 -1 4 3 -1] 1 2 4 x -8 2 6x -9 -3 3x…

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Q: Find the matrix of the quadratic form. 2 4x1 + 6x +3x3-10x1x2 + X2X3 Select one: O A. O B. C. O D.…

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Q: Solve the matrix by using Cramer's Rule method 2x+5y+2z=10 3x+8y+z=3 2y+5z=1

A: To solve the matrix by using cramers rule method.

Q: 5. Use the matrices to solve the x-2y+3z = 4 system: 3x- 4y+z = 4 2x +3y-4z = -2

A: We have to solve the equation by matrix method.

Q: find a 3 x 1 matrix x with entries no all zero such that Mx = 1x and            [ 1 2 -1 M =…

A: Consider a system of homogeneous equations. A system of equations can be solved by eliminating some…

Q: s described by the equation Systam x= Ax where A = -1 -2 1 -H Assuming madrenQ on the stability of…

A: Given matrix : A=-1-21-4 Also, Q is a unit matrix. Thus, Q=1001 Given equation: ATP+PA=-Q Here,…

Q: 2. Write the quadratic function f(x,,y;)=-3x; +2x,x, – 3x; – 4x, – 4x, +6 in matrix form as f(x) =…

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Q: Q1/ Find the matrix below: -5x+2y-4z=5 3x+5y-2z=0 -2y-8z=3

A:

Q: I1,I2,I3 of th

A: Here we have;  11I1+4I2+3I3=-4-15I1+4I2+4I3=163I1+4I2+17I3=3 let;  AX=B  where  A=1143-15443417,…

Q: (d) Write down the matrix of the quadratic form Q(x1,x2, 3, x4) = x +2x3 – 7x3 +xỉ – 4x)x2+ &x,x3-…

A:

Q: 6 X1 -1 -5 X2 II

A: Let us consider the system of differential equation X'=AX then the solution of system of equation is…

Q: 2. Solve for X in the given matrix equation (A – X) =B where A = 3 2 -1 ol and B = MIN2

A: We have to find X

Q: Express the quadratic form as v Av, where A is a symmetric matrix. x² + 3y² + 5z² - 4xy+3yz + 10xz

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Q: Solve for unknown matrix X in the matrix equation X +3A=B where: -5 4 A = -3 7 2 6 -7 12 7 0 X = 4 3…

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Q: 10. Find the simetric matrix for the quadratic form Q(x1,x2,x3) = xỉ + 3x + x,x2 – x1x3

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

Q: 1. Identify the two-by-two matrix with matrix elements a;j = i – j. O (1 (금) ㅇ(9) (오 ㅇ (? )

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Q: • The Matrix B from 3 x 2 at b, = -1+; is го 1. 2.

A:

Q: Find the symmetric matrix A associated with the given quadratic form.

A: To determine: The symmetric matrix A associated with the given quadratic form. 5 x12 - x22  + 2 x32…

Q: Use Cramer's Rule to solve the 3 x 3 matrix A- 3B + 7Z = 13 A +B +Z =1 A- 2B + 3Z = 4

A:

Q: Reduce the quadratic form 3x2+5y2+3z2-2yz+2zx-2xy into a canonical form of the matrix.

A: Given quadratic form 3x2+5y2+3z2-2yz+2zx-2xy.

Q: Given the matrices A=[0235], B=[2−2 4−2] and C=[5−5 0 2],,solve for the matrix X in the equation…

A: We have to find matrix X