Given n >1, show that the set of all 1 x n matrices of positive integers is countable.

Q: Find x such that the matrix is singular. A = -3 -2 X =

A: Given A = 6x-3-2

Q: If A and B are n × n diagonal matrices, show that AB = BA.

A:

Q: Show that an n x n nonnegative matrix is transitive if and only if £=1 4* is a positive matrix. -k=1

A: Given that, An nonnegative matrix is transitive.…

Q: Find conditions on a, b, c, and d such that B = as attached commutes with every 2X2 matrix

A: B=abcd Let A=uvxw BA=au+bxav+bwcu+dxcv+dwAB=ua+vcub+vdxa+wcxb+wd Let BA=AB…

Q: Consider 4 x 4 matrices A and B and the following patterns from each. Ho ons are +here for each…

A: Given:  Let  P1=3000020000010010  & P2=0100002020000002

Q: Find x such that the matrix is singular. X 3 A = -7 2 X =

A: Singular Matrix - A matrix is said to be singular if and only if its determinant is equal to zero.

Q: Let A and B be n × n matrices. Show that if AB is nonsingular, then A and B must be nonsingular.

A: Matrix: Let Ab is nonsingular. Therefore ABx=0 has only the trivial solution. Now let b be singular…

Q: Find two different 2 × 2 matrices A such that

A: Given:               A2=1001

Q: Let A and B be symmetric n × n matrices. For eachof the following, determine whether the given…

A:

Q: Given a positive integer n, compute the nth power of the matrix A =

A: First find some powers of A then find a pattern and get a formula to get any power of A

Q: Let X be any n x k matrix. Show that X'X is a symmetric matrix.

A:

Q: Give an example of a nonzero 2 X 2 matrix A such that A2=O

A:

Q: Find a 3 x 3 matrix A such that 1 -5 A 3 A 1 -3 and -2 A 4 1 -5 A = 3. ||

A:

Q: Let A and B be symmetric n × n matrices. For eachof the following, determine whether the given…

A: Given that A and B is a symmetric matrix: Here the objective is to determine whether D is symmetric…

Q: Find a matrix A such that [is: is a solution for AX=X'.

A:

Q: Find x such that the matrix is singular. [ х 3 A = -9 8 X =

A: The given matrix is: A=x3-98

Q: Let A and B be two skew-symmetric matrices of the same size. Show that AB+BA is symmetric.

A: Given that: Let A and B be two skew-symmetric matrices of the same size. To show: AB+BA is…

Q: [:] Suppose A is a 2×3 matrix such that A and A -3 Compute the product A

A: I have writen the vectors in linear combination of given two vectors and applied A in both sides

Q: Let A be an n × n matrix in which the entries of each row sum to zero. Find ∣A∣.

A:

Q: 13. Find all 2 x 2 matrices A = such that A? %3D

A:

Q: If A and B are square matrices of the same size such that AB = BA, prove that (AB)2 = A2B2.  By…

A:

Q: Let A be an n × n singular matrix. Then

A: if matrix A is singular that means its determined is zero.so at least one row of matrix A is…

Q: Let A, B and C be square invertible matrices of the same size. If BTB=I=BBT(XT is the transpose of…

A: A square matrix is said to be invertible if their inverse exists that is determinant of matrix is…

Q: If A is an n × n matrix, show that (Ak )T = (AT )k for any positive integer k.

A: Matrix: We will solve it by the method of induction:(Ak)T=(AT)k case 1: k=1case 2: k=ncase 3: k=n+1

Q: Let A be an n × n matrix in which the entries of each row sum to zero. Find det(A).

A:

Q: Find two 2 × 2 matrices A such that A2 = I.

A:

Q: Let p(x) = x³ – 2x + 4 and compute p(A). |2 A = |0 -3 4 NOTE: Write the elements of the matrix…

A:

Q: Find nonzero 2 × 2 matrices A and B such that AB = O.

A: Consider

Q: Construct a 3 × 2 nonzero matrix A such that: Ax = 0 has only the trivial solution.

A:

Q: Determine all the n × n− matrix A with the range such that A2 = A.

A: Clearly the zero matrix and identity matrix are the trivial examples of our problems. However there…

Q: Find two different 2 × 2 matrices A such that A2 = O .

A: Let A=abcd be the 2×2 matrix.

Q: Let A and B be n × n matrices and let C = A − B. Show that if Ax0 = Bx0 and x0 = 0, then C must be…

A: Consider the A and B are n×n matrices and C=A-B. If x0=0, Ax0 =0 and Bx0 =0 are nontrivial…

Q: Let A be an n × n symmetric, positive definite matrix. Show that if P is any n × n nonsingular…

A:

Q: Let A be an n ×n matrix and B= A + I, where / is the identity matrix, then it is possible for A and…

A:

Q: Suppose that A is an n × n matrix and det A + 0. Determine the rank and nullity of A.

A:

Q: Show that for any n x n matrix A there exists another n x n matrix M such that MAM-1 = AT, where AT…

A: Consider the given information. Let the matrix A is an n×n matrix and M is a m×m matrix. And the…

Q: Find a 3 x 3 matrix A such that Ax = 8x for all x in R³. A =

A:

Q: Let X be a set of 2x3 matrices. if for any

A:

Q: Show that if A and B are similar matrices, then Ak and Bk are similar for any positive integer k.

A: Given:          A and B are similar matrices   To prove:            Ak and Bk are similar for any…

Q: Let A be an n × n matrix and let B = A + AT and C = A − AT (a) Show that B is symmetric and C is…

A: given: let A be a n×n matrix. B=A+AT C=A-AT we have to show that B is symmetric matrix and C is skew…

Q: Find two 2 × 2 matrices A such that A2 = O.

A: to find a matrix A

Q: 13. Find all 2 x 2 matrices A = (" such that A? %3D

A: Image is attached with detailed solution.

Q: Let A and B be symmetric n × n matrices. For eachof the following, determine whether the given…

A: Given,  A and B be symmetric n × n matrices i.e.  AT=A    and  BT=B And E=AB

Q: Find x such that the matrix is singular. A = -3 -6

A:

Q: Prove that every 3 x 3 matrix is a linear combination of invertible matrices.

A: A square matrix is invertible if and only if the determinant of the matrix is not equal to zero.…

Q: Find a 3×3 matrix A such that  Ax=4x for all x in R3.

A: To find a 3×3 matrix A such that Ax=4x for all x in R³

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.