2. Write the following in vector/matrix notation, specifying all components of the matrices. If it cannot be done, state why. (a) xí = 9x1 – 3x2 + e°, X = 3x1 + 9x2 + 5 cos(t). (b) x = 9x1 – 3x1x2. x = 3x1 + 9x2. (c) x = 9x1 – 3x2, X½ = 3x1 + 9x3.

Q: Use the definition of Ax to write the vector equation as a matrix equation. 3 - 4 4 9 - 3 + X3 3 %3D…

A: We will do this by using definition of augmented matrix

Q: 1. Find the cofgctor of 6 in matrix B. 4 り り

A: We will find out the cofactor of 6 for given matrix B.

Q: Give a matrix representation of the quadratic form f(x, y, z) = 4x 2 + 9y2+ 16z 2 − 2xy + 4xz − 6yz…

A: Given: f(x,y,z)=4x2+9y2+16z2-2xy+4xz-6yz             We have to find a matrix representation of the…

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

A: Solution: Consider the given quadratic form is: 2x2 - 3y2 + z2 - 4xz we know that if ϕ =…

Q: If Q = I - auu" where Qis an orthogonal matrix, a > 0, and u E R"X1 real vector, and I is n x n…

A:

Q: 4. Determine whether the given matrix is invertible without computing its determinant. -3 0 1 3 5 8…

A:

Q: (4) For the zero-one matrices A = and B = calculate %3D 0 0 1 1 (а) АЛВ (Ъ) АоВ (с) ВОВ

A: 4) Note:  AΛB = [aijΛbij] =[aijbij] , known as meet of A and B, only possible if matrix have same…

Q: Solve for the matrix X if AX(D+BX)~' = C. Assume that all matrices are n X n and invertible as…

A: Given that AXD+BX-1=C Pre-multiply by A-1 A-1AXD+BX-1=A-1CXD+BX-1=A-1C post multiply by D+BX…

Q: Find values for the variables so that the matrices are equal.

A: Given that the matrices are equal. x4=6y

Q: V2 1 2 11 T = 0- 2 000 -Vī

A: If A is a matrix of order and I is the identity matrix of order, then If A-1 is the inverse matrix…

Q: c) [For Susan Foreman of 76 Totter's Lane, Coal Hill School, 1963, WHO Could See This] A a 5x5 real…

A: A be a matrix 5 * 5  We have to find the matrix A and also find the geometric description of A and…

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: 1 : Find the inverse of the matrix 1 -1 0 A = 3 -1 2 with using the method of Cofactor (Adjoint).

A:

Q: Consider the following matrix and vector: 1 1 A = 1 -4 0 -3 -2 and x = 6

A:

Q: If you know all 16 cofactors of a 4 by 4 invertible matrix A, how would you find A?

A: Given, an invertible square matrix A of order 4, and we know all the 16 cofactors of this matrix.…

Q: Suppose (B-C)D=0, where B and C are mxn matrices and D is invertible. Show that B = C.

A: The given matrix equation is B-CD=0 B and C are the matrices of the order m×n while D is the…

Q: Consider A and B are two square matrices and B is a scalar. Calculate (BA^T B)^(-1) = *

A:

Q: Find all pairs (x,y) for which matrix B is not invertible, where 1 1 B = 2 1 1 0 -1 y

A: Here we will apply the condition for a matrix not being invertible to solve this question that is…

Q: Suppose that T() and 7 () -E Find the standard matrix A for Tand find T(:) 14 and 2 and T (HD A-3…

A:

Q: Due to what property, applied to the matrices and scalars below, do we know that (cd)A = c(dA)?

A:

Q: which of the following is the cofactor A13 of matrix?

A: Simply omit that raw and column whose co-factor matrix required and write rest all elements in same…

Q: Find the change of basis matrix from B2 to B1. -4 B1 = , B2 B2 = 2

A: The change of basis matrix C from B2 to B1( or from the basis B2 to the basis B1 ): β1=-142,231  and…

Q: Examine the nature of the following matrix defined by A = [0        1 + 2i       −1 + 2i      0  ]…

A: Given:  A=01+2i−1+2i0 To explain nature of above matrix and to find its proper values and proper…

Q: Solve the equation (X – A)B = BC for X, assuming A, B, and C are all invertible (note that A, B, C,…

A:

Q: 6. Find the distance between the matrices A and B, p(A, B), using the ||- ||2 for the matrix -[:] -1…

A:

Q: Find inverse of matrix A by Gauss-Jordan me [2 -1 2

A: Here we have to find the inverse of the matrix by the Gauss-Jordan method.  we have,

Q: The equatiokn  Y = (x,y)T  is given as a vectorfunction with 2 components and A = table below 3 2 2…

A: Given is a matrix A and we have to diagonalize the matrix A. First we find eigenvalue of matrix A…

Q: Find the Jacobi matrix for the following function. 5x + 6у f(x, y) = 5x - 4y? Jacobi matrix, (Df)(x,…

A: Given : f1(x, y) = 5x+6y f2(x, y) = 5x²-4y² To find : Determinant of jacobian matrix

Q: For the quadratic form x²+ xz - 6yz = 0 in the matrix notation X'AX the matrix A is: 1 1

A:

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: 12. Find two different 3 x 3 matrices A and B such that the associated quadratic forms equal q(7) =…

A:

Q: 2 In what direction does f(x) = 7xy - 9x increase most rapidly at (4, - 1)? V f(4, - 1) = (Type an…

A: I am attaching image so that you understand each and every step.

Q: Use the definition of Ax to write the vector equation as a matrix equation. 7 4 2 9 +X3 +x2 HOO -9 9…

A:

Q: Solve for the matrix X if AX(D + BX)-! = C. Assume that all matrices are n X n and invertible as…

A:

Q: Due to what property, applied to the matrices and scalars below, do we know that c(A + B) = cA + cB…

A: Given: We have to state which property for c(A + B) = cA + cB and (c + d)A = cA + dA

Q: and Y = (1 1 -) If X =0 1. Find the matrix Z where Y = Xiz %3D -2

A:

Q: (-9,6) Use matrices to reflect the vector the line y = x. ove

A: Topic:- algebra

Q: It's given that A,B are invertible matrices and A is also symmetric. If C =BA , D=AB and…

A:

Q: Using only 0's and l's, find the number n of possible 3 x 3 matrices in row canonical form.

A: We have to make all possible row echelon form ( row canonical matrices ) of 3×3 matrix with 0 and 1…

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

A:

Q: Consider the following matrix and vector: 1 1 A =|-2 0 -3 1 1 -4 and x = X2 6. x3 Given that Ax=0…

A:

Q: nd the inverse of the matrix 1 0 -2 1 4 -3 4 oices: 8. -3 1 8 3 1 а. 10 4 1 C. 10 4 1 -7/2 3/2 1/2…

A:

Q: Consider the 3 x 3 matrix 1 2 3 A = b а -1 2 3 where a, b and c are some unknown scalars. If…

A: We are given a matrix: A=123abc-123 we need to find a, b and c such that A13 =24, A12 =-19 and A33…

Q: Using Laplace expansion, the 4x4 matrix will be reduced to 4 terms with a 3x3 minor determinant.…

A: Answer is mentioned below

Q: Consider the following matrix and vector: - El 1 1 and x = 1 -4 0 -3 A = -2 1 X3 Given that Ax=0 and…

A:

Q: Consider a 3 × 3-matrix whose first row is a vector a, the second row is a vector b, and the third…

A: given row  of  3×3  matrix  is          a   , vector      b   , vector c=2a+3b    , vector

Q: 3. Verify that the following statement is true for these matrices: (XY)-1 = Y-!X-!. A suggestion:…

A: