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 possible find the unknowns a, b and c if it is given that A13 = 24, -19 and A33 = 0. A12 =

Q: If X is a rankr matrix, show that the two square matrices XXH and X#X have the same nonzero…

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Q: It is possible for a 3 x 3 matrix A with eigenvalues 1 3,-3 + i, -2 + i.

A: Solve

Q: Find a (2x2) singular matrix A that maps (2, 4) into (3, 1).

A: Singular matrix mean its Determinant is equal to 'zero' .

Q: - 3 6 - Given A = 27 , find one nontrivial solution of Ax = 0 by inspection. [Hint: Think of the…

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Q: Express the invertible matrix (1 2 1 10 1 1 2) 1 as a product of elementary matrices.

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Q: Suppose that A is 2x2 matrix with eigenvectors V, = which correspond to A, = 3, 12=2 respectively.…

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Q: Suppose A is a 6 x 6 matrix with eigenvalues A = 2, 2, 2, 2, –3, -3. (a): What is the determinant of…

A: Given: Suppose A is a 6x6 matrix with eigenvalues 2,2,2,2,-3,-3

Q: 2. For the matrix 2 2 -1 B -3 3 find its Pseduoinverse Bt and the 2-norm ||B*||2.

A: Given : B=212-1-1-3-13 To find : pseudoinverse B+ and the 2-norm ∥B+∥2

Q: Find a 2 x 1 matrix x with entries not all zero such that 2 Ax = 3x, where A = 1 2

A: Given matrix is A=2   11   2 and condition is Ax=3x

Q: Find an LU factorization of the matrix A (with Lunit lower triangular). 4 A= 12 2 -0 12 8 4,

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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: If A is a 3 x 3 matrix which has eigenvalues 2 = 1, a Then A is diagonalizable 2, and 2 = –3. False…

A: 7. As if in a matrix all the eigen values are distinct then the matrix must be diagonalisable.

Q: -14] is a linear combination of the vectors 16 if and only if the matrix equation Az = b has a…

A: Solving

Q: It is possible for a 3 x 3 matrix A with eigenvalues 2 = 3,-3 + i, -2 + i.

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Q: The eigenvalues of a 3x3 matrix A are -4,2,9. Find the determinant of (A-1)T

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Q: [1] Construct a 3 x 3 nonzero matrix A such that the vector |2 is a solution of 3. Ах 3D0

A: A vector is given let x=123 To find: A non-zero 3×3× matrix,A=a11a12a13a21a22a23a31a32a33

Q: Find 6×6 matrix a, that satisfies the stated condition. Make your answers as general as possible by…

A: Let the genral 6*6 matrix is given by…

Q: Find a 3 × 1 matrix x with entries not all zero such that

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Q: Find the characteristic equation of the matrix by inspection. 2 -5 9 6 -3 0 0 4 0 0 8

A: Given that: 2-5960-30000400008 The characteristics equation is given by the formulas, detA-λI=0

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: Suppose A and B are similar, do the matrices A? + A + I and B? +B + I still have the same…

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Q: For an NxN-dimensional matrix A, prove that a) the product of the eigenvalues is equal to the…

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Q: A- -2 21 -2 31 -2 2 31 -2 3 2 B = -4 2 5

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

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Q: Prove that the quadratic equation A^2 - 3A = 2I hold true for the matrix A =  5  -6  -6        -1…

A: The detailed solution is as follows below:

Q: The matrix (matrix image) has one eigenvalue equal to 3. The sum of the other two eigenvalues is...…

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Q: Show that the matrix; is singular

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Q: Suppose that A is 2x2 matrix with eigenvectors V, = which correspond to A,=3, 1,-2 respectively.…

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Q: If the eigen vectors of a 2 x 2 matrix A corresponding to the eiger -- 2 respectively then the…

A: The Eigen vector corresponding to Eigen value -1 is 11 The Eigen vector corresponding to Eigen value…

Q: If the diagonal matrix that is congruent to the given matrix is  2 0 0 0 -1 0 0 0 0 Can we…

A: Given matrix is A=−101011011. And the diagonal matrix that is congruent to the given matrix A is…

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

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

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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: Find the inserve if it exists, of the following matrix. 1 2 1 1 1 2

A: The give matrix  is, 1 1 -1 2 -1 1 1 1 2 The determinant of the above  matrix is,…

Q: Suppose A is a matrix with eigenvalues A1 = 1, A, = 2, A3 = -3, with corresponding eigenvectors v1…

A: Given: A is a matrix with eigenvalues λ1=1, λ2=2, λ3=-3 with corresponding eigenvectors v1=001,…

Q: Let r1, .. r,be vectors in R", and let Q be an m xn matrix. Write the matrix Qr, Qr, as a product of…

A: Given:Let r1.......rp be vectors in ℝnLet Q be an m×n matrix Qr1.......QrpR=r1.......rpQ=Q…

Q: Suppose A is a 3x3 matrix. Let B be the matrix obtained from A by performing the following…

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Q: с pose the vector -6 is in the nullspace of the matrix d 6 -4 34 1 -5 23 1 -7 rmine c and d giving…

A: Topic:- application of algebra

Q: Find a 3 x 3 matrix A whose -4-eigenspace is and whose 3-eigenspace is A = V = {(x, y, z) in R³ |…

A: To Find: a 3×3 matrix whose 4-eigenspace is V=x, y, z in ℝ3 | -8x-14y+10z=0 and whose 3-eigenspace…

Q: If matrix A is square of size n x n with a rank equal to 2 and n > 2. The rank of a matrix is equal…

A: Given that, matrix A is square of size n×n with a rank equal to 2 and n>2. the rank of a matrix…

Q: Find 2x2 invertible matrices A and B such that A + B not equal to 0 and A + B is not invertible.

A: Wee need to find matrix A and B and do their addition and find invertible

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: Q3, Write any matrices A and B of order 3 x 3 and verify the results Let A and B be n x n matrices,…

A: Write any matrices 'A' and 'B' of order 13×3 A=110012003    B=013100100 To verify 1)…

Q: It is possible for a 3 x 3 matrix A with eigenvalues 2 = 3,-3+i,-2+i. 10

A: Need to find true false

Q: Let A be the 2 x 2 matrix with elements a,, a12 = a21 = + 1 and a,, = - 1. Then the %3D eigenvalues…

A: Introduction :Given , a matrix A with elements and we have asked for the eigen values of matrix A19

Q: Let A be a 3x3 matrix with eigenvalues 1,-1,3. Then which of the following is non-singular matrix…

A: According to the problem A is a 3×3 matrix with eigenvalues 1 , -1 ,3For example consider   A…

Q: ind LU and LDU factorization of the following tridiagonal matrix. A=[1 1 0; 1 2 1; 0 1

A: Given matrix is  A = 110 121 012 To find the LU and LDU factorization of the given matrix.

Q: 5. Show that the condition that the block matrices (8 ) m ( ) A 0 А С and B В can be matrices of the…

A: Given: The block matrices, A00B and AC0B.   To show: The given block matrices can be matrices of the…