2 2 1 2 -1 2 is orthogonal. Verify whether the matrix A = 3. -1 2 2

Q: Use the definition of Ax to write the matrix equation as a vector equation. 0 -9 -4 - 3 1 8 2 6 3 4…

A: Use the definition of Ax to write matrix equation as a vector equation. 01-98-4-6-3-423=36-26-18…

Q: 3. Express this system of equations in matrix form. a1 – b, P1 + e, P2 -c, + d,P Qai Qs1 Qai Qsl Qa2…

A:

Q: True or false? det1A2 is defined only for a square matrix A.

A: True or false. det A is defined only for a square matrix A.

Q: True or False: The following matrix is diagonalizable. 1 -0 -2

A: For the solution follow the next step.

Q: Show that rows and columns of the given matrix are orthogonal? 2 -1 6. V13 V5 39 -2 7. L = İV13 V5…

A: Orthogonal matrix: A square matrix A is called orthogonal matrix if AAT = I = ATA. If a matrix A is…

Q: Find all the vectors b e R such that the linear system A7 = b is consistent, where the coefficient…

A:

Q: Write the third column of the matrix as a linear combination of the first two columns, if possible.…

A:

Q: [-5 -5 [-3] 1. For the matrix A 2 -3 determine (and explain why) if vector ú 3 is | 4 2 3 2 a. in…

A: GIVEN A=-5-5002-3423 to determine if vector u→=-332

Q: 3 Compute x using the vectors w = -4 and x = 2 - 5 2 x = (Simplify your answer. Type an integer or…

A:

Q: 3. 14. 7. -3 -10 7. -12-13 13| 151 14 5. -3 13 |-15 -13 14 7. 11 3. -3 13 14 11 15 7. -13-10 7. -12…

A:

Q: Find the diagonal line matrix P 7 -5 0 4 -1 A = 2 8 -3

A: Given the given matrix is A=57-504-128-3

Q: c. Find an orthogonal diagonalization of the symmetric matrix 1 -2 0 A = -2 1 4

A:

Q: Write the third column of the matrix as a linear combination of the first two columns, if possible.…

A:

Q: snip

A: The determinant of an orthogonal matrix is always one. Therefore to prove that the given matrix,…

Q: Rewrite the simultaneous linear equations above b. Hence, calculate the inverse of the above matrix.…

A:

Q: Diagonalize the given matrix if possible: A = [1 2 0 -1

A: Our Aim is to diagonalize the matrix A=120-1

Q: 5. Determine whether or not matrix. A shown below is orthogonal and justify your answer. 10 0 1 30…

A:

Q: 2 -2 5. Let B = Find a matrix P that orthogonally diagonalizes B. -2 -1

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Q: Write the third column of the matrix as a linear combination of the first two columns, if possible.…

A:

Q: 1 1 -3 Is the matrix A = 1 5 -2 positively definite? Justify your answer. -3 -2

A: Sylvester's criterion states that a Hermitian matrix A is positive-definite if and only if all the…

Q: Which matrix is not orthogonal? 1 00 0 1 1 0 0 0 1 V2/2 -V2/2 0 -v2/2 V2/2, 0 V2/2 -V2/2 0 v2/2…

A:

Q: [1 0 2] 1 2 is diagonalizable. Justify your answer. 0 0 0 9. Determine if the matrix A = 1

A: If minimal polynomial having a repeated roots then that matrix is not diagonalzible.

Q: Find an LU-factorization of the matrix: show solutions. 1 1 a. 1 ⠀⠀ 2 2 2 3 2 5 b. 6 14

A:

Q: Write the third column of the matrix as a linear combination of the first two columns, if possible.…

A: This is based on application of Matrix.

Q: (3) 2 -2 5. Let B = Find a matrix P that orthogonally diagonalizes B. %3D -2 -1

A:

Q: [2 0° 0 3 2. similar to matrix 1 ? 0 3 Is matrix

A: The matrices A and B are similar if there exists an invertible matrix P such that B=P-1AP

Q: Orthogonally diagonalize the matrix 1 2 2 -2

A: Given,     122-2

Q: The vector -201 3 is a linear combination of the vectors 10 5 -3 and -9 if and only if the matrix…

A: Answer is in next step.

Q: True or False: The following matrix is orthogonally diagonal 4 2 -1 2 3 7 -1 7

A:

Q: Use the definition of Ax to write the vector equation as a matrix equation. - 6 8 - 1 - 9 5 3 X1 - 2…

A:

Q: 1 If A = a %3D then A is an orthogonal matrix when a. a = ±2 O b. a = ±1 %3D O c. a = ± d. α- +3

A:

Q: a2 If the columns of the matrix A = -1 are orthogonal, then 2 -1 2 az = 1 a. O b. az = -1 C. a3 2 d.…

A: If column of matrix  A are orthogonal then  B = A^T A  Elements B(i,j) = 0 for i is not equal to j.

Q: [2r2 – 3r1 21 - 4x2 6. Show that T is linear by finding its standard matrix given that T(|

A: Let's convert this into equation form. The matrix derived by arranging the coefficients of x1 and x2…

Q: Orthogonally diagonalize the matrix -1 -2 1 2 3 | A = 1 -2 -1 1

A: The given matrix is: A=3-1-2112-2-11

Q: Write the column vectors and row vectors of the given matrix. 1 13 4=-1-2 2 6

A: Given matrix is :

Q: Q.3: Express the matrix as a product of elementary matrices 2 0] [1 1 3 A = |0

A: Explanation of the solution is given below...

Q: Use the definition of Ax to write the matrix equation as a vector equation. - 4 -7 - 20 -5 8 -2 42…

A:

Q: (BH) Recall that a matrix Q is orthogonal if Q' Q = I.

A: Given, A matrix Q is orthogonal if QTQ=I Proof: (a) The one way to write the norm for vector x is…

Q: Matrix AA is transformed by a scalar to form matrix BB . A=[−1.5   3]       B=[3   −6] [4.25…

A:

Q: Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal mama Da 15) 10-61…

A: The given matrix is                                      10-6-65

Q: 2 -2 5. Let B = . Find a matrix P that orthogonally diagonalizes B. -2 -1

A:

Q: Write the third column of the matrix as a linear combination of the first two columns, if possible.…

A:

Q: Orthogonally diagonalize the matrix 1 -1 -2 A -1 2 -2 3

A: Given:   A = 1-1-2 -120 -203

Q: Diagonalise the symmetric matrix A = 4 2 2 2 4 2 2 2 4

A: Given symmetric matrix is  We have to diagonalise the above matrix. First we will find the…

Q: Show that rows and columns of the given matrix are orthogonal? 2 6. 13 39 -2 7. 7. V13 39 4. -3 8.…

A: Given the matrix is L=213-15639313-25739413-35839

Q: Show that rows and columns of the given matrix are orthogonal? 2 -1 6. V13 V5 V39 -2 7 L = V13 V5…

A:

Q: Write the third column of the matrix as a linear combination of the first two columns, if possible.…

A: Given matrix- 121556438964 We need to write third column of matrix as a linear combination of the…

Q: 2. Orthogonally diagonalize the matrices. -4 4 1 5 (a) 5 1 (b) |-4 4 9

A: The given matrices are; a)  1 5       5 1 b).   7  -4  4        -4  5  0         4  0  9

Q: erom these equation,calculate V3 by the matrix 2 -3V2+oV1 = 240 2-3V1+ 172=0 3-2V2 +5V3 こ0

A: See the details solution in below

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.