2. State a, , the leading diagonal of matrix and the order of the matrix for matrix a) 4- (5) b) 3 -) b) В -

Q: Show that the matrix is not diagonalizable.

A: Solve for det(A - λI) = 0

Q: Suppose that A is a 18 x 7 matrix and the null space of A has dimension 3. What is the rank of A?

A: For a m×n matrix, the number of rows is equal to m and the number of column is equal to n .

Q: Let A = [aj be a 4 x 4 matrix. Develop the general expression for det(A).

A: Given:               Matrix A is : [aij] is the 4×4 matrix;   General expression for the determinant…

Q: hat is a matrix

A: Matrix:

Q: A square matrix in which all elements except at least one element in diagonal are zeros is said to…

A:

Q: Show that if A is an upper triangular matrix, then A T is lower triangular.

A: A is an upper triangular matrix. That is, Now let A=aij be a n×n upper triangular matrix. Then,…

Q: Show that a square matrix which has a row or a column consisting entirely of zeros must be singular.

A: Consider a square matrix A=000123456 and B=140250360 Here, all the elements of first row of the…

Q: If A is a rank one matrix, the second row of R is ___ . Do an example.

A:

Q: Define Triangular matrix ?

A:

Q: Show that if A is a symmetric matrix, then Ak , k = 2, 3,... , is symmetric.

A: Given that, A is a symmetric matrix. Then we get, A^T = A; where A^T is the transpose of matrix A We…

Q: Calculate the rank of each matrix by converting it into canonical form…

A:

Q: Find a matrix P that diagonalizes A

A:

Q: Prove that (A + B)² = -(A + B) in matrix..

A:

Q: Show that eA is nonsingular for any diagonalizable matrix A.

A:

Q: Consider the matrix

A: Given, the matrix                A=0-3-1020233 And the eigenvalues of A are λ=1, and λ=2.

Q: whether the matrix is in reduce

A: The matrix is given as  , 190-10001500000100000 1. The condition for row echelon form (ref) is The…

Q: It exists, Ol the matrix. 1 - 1 2 – 1 1 1 1 2

A: A-1=?

Q: ГО 5 4 5 1 2 2 3] A = [1

A:

Q: Let A be a 3x6 matrix of rank 3 then nullity of A equal 0 Select one: O True O False

A: From rank plus nulity theorem we know that : rank A + nullity A = the number of columns of A  From…

Q: (2) Let A = UDV" be a SVD of a square matrix A. What is the sum of squares of the singular values,…

A: We find the sum of squares of the singular values in terms of A.

Q: Explain why the row vectors of a 8 × 7 matrix form a linearly dependent set. (Assume all matrix…

A: Consider the given information. The given matrix in the form of 8 *7 matrix, forms a linearly…

Q: Show that the matrix below does not have an LU-factorization.

A:

Q: Let A be an m x n matrix. Is ATA symmetric? Explain.

A: Given that, A is an m×n matrix

Q: What does it mean to say that A is a matrix with dimensionm  n?

A: A matrix is a rectangular array of elements arranged in rows and columns. The size of the matrix is…

Q: suppose A be any Hew of have symmetric matoir order and this matrix 4x4 rank of 3 the caleulata the…

A:

Q: Can the null space of a 3 × 6 matrix have dimension 2? Explain.

A:

Q: Let E be the elementary 3 x 3 matrix corresponding to the elementary row operation of multiplying…

A: Elementary matrices: Elementary matrices are n×n square matrix which is obtained performing…

Q: Determine the dimension of the matrix. 3 -9 4 -8 -6 7 10 6 1

A:

Q: 2. Determine the matrix X, such that:

A: Solution:-

Q: Prove that a 2×2 matrix transforms any straight line into a second straight line and points on the…

A: Let the 2×2 matrix be A=a11a12a21a22 which is the matrix of a linear transformation T:ℝ2→ℝ2. Let the…

Q: Show that the matrix B′AB is symmetric or skew symmetric according as A is symmetric or skew…

A: Show that the matrix B′AB is symmetric or skew symmetric according as A is symmetric or skew…

Q: Prove that the nonzero rows of a matrix in a row echelon form are linearly independent

A:

Q: 2. Let the rref of a matrix A be, 0 2 0 -2 0 1 -5 0 -3 0 0 0 1 6 Determine A if the first, second…

A:

Q: Show that if the matrix X is diagonalizable, then X" is also diagonalizable.

A: Given that the matrix X is diagonalizable. We have to show that XT is also diagonalizable. Since,…

Q: Prove that ||A||₁, ||A||, || A||₂, are matrix norms.

A:

Q: Find a matrix P that diagonalizes 1 0 0

A:

Q: Consider the matrix A =

A: Given, the matrix                       A=420040004

Q: Let A be a 3x6 matrix of rank 3 then nullity of A equal 0 Select one: True False

A:

Q: Let A be a 3x6 matrix of rank 3 then nullity of A equal Select one: True False

A: Given A is a 3×6 matrix of rank 3, then nullity of A is zero. We need to check whether the given…

Q: A matrix in which there is only one row and any number of columns is said to * .be matrix

A: Given:     Expression is ^-*33*425       In the prefix form of an expression, a binary operator…

Q: Show that (-A) T= -A", where A is a 2x3 type matrix (you can show it on the example)

A: Let matrix A=abcdef. Order of matrix A is 2×3. ⇒-A=-a-b-c-d-e-f ⇒(-A)T=-a-d-b-e-c-f  →Result 1

Q: Prove that deleting the last column of an echelon form (respectively, the row canonical form) of an…

A: Echelon matrices come in two forms: the row echelon form (ref) and the reduced row echelon form…

Q: [5 Let B =E dl: Is the matrix B orthogonally diagonalizable? If yes, find a diagonal matrix 2 0…

A:

Q: Prove that A4, A||, ||A||₂ are matrix norms.

A: Given: ∥A∥1, ∥A∥∞, ∥A∥2 To prove ∥A∥1, ∥A∥∞, ∥A∥2 are matrix norms.

Q: Show that the matrix is not diagonalizable.

A: Given matrix The characteristic polynomial of is the only Eigen- values are

Q: If A EM,C {c} such that A2 = A. Prove that A is not a strictly diagonally matr. the last word is…

A: A square matrix is said to be strictly diagonally Matrix if all entries are zero except diagonal…

Q: show that the matrix П (I2 + 03) ® I2 is a projection matrix.

A: A matrix is a set of numbers organized into a predetermined number of rows and columns. The numbers…