Let O be the k x k matrix whose entries are all 0, 1 be the k x k identity matrix, and B be a k x k matrix with the property that B = 0. If A= [ ) determine the block form of A-+A² +A.

Q: Let A be an m x n matrix with m < n. Which of the following statements is always false?

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Q: Let A be a m×n matrix. Prove that AB and Ba both exist only if B is an n×m matrix.

A: Explanation of the answer is as follows

Q: Let A be an n × n matrix. Show that rank A = n if and only if the columns of A are linearly…

A: Show that rank A = n if and only if the columns of A are linearly independent.

Q: If B is a matrix obtained by multiplying each entry of some row of a 2 × 2 matrix A by the scalar k,…

A:

Q: Let A = XYT, where X is an m × r matrix, YT is an r × n matrix, and XTX and YTY are both…

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Q: If A is an m xn matrix, then A and AA have the same rank. O True O False

A: Consider the statement  If A is an m×n matrix  then A and ATA have the same rank

Q: Let A be an m × n matrix. Show that A is row equivalent to O if and only if A = O .

A: Consider the given information as A be an n×nmatrix

Q: Let A and B be nxn inversible matrix. Prove that AB is invertible and (AB)-1=  B-1A-1.

A: Let A and B be n x n invertible matrices, with inverses A-1 and B-1, respectively.

Q: Let = Find a nonsingular matrix P and a diagonal matrix D such that P-'AP = D.

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Q: Let A be an m ×n matrix and B be an n ×p matrix. Prove that AB can be written as a sum of n matrices…

A: Given that A be a mxn matrix and B be a nxp matrix.Now, prove that AB can be written as a sum of n…

Q: Show that if A is a nonsingular matrix, then adj A is non- singular and 1 (adj A)- = A = adj(A-).…

A: Given: A is a nonsingular matrix. Since A≠0

Q: Let A be a matrix whose entries are integers, and det A=1. 4 : Show that the entries of A-1 are all…

A: given ,det A = 1

Q: If A is an m x n matrix then A' A and A have the same rank. true false

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Q: Determine whether the given matrix A is diagonalizable. If so, find a matrix P that diagonalizes A…

A: Given matrix A=01-12 and A=200121-101To find: A matrix P that diagonalizes A and a diagonal matrix…

Q: let Q(x)= x12 -8x1x2 -5x22 , then matrix A of the quadratic from is A=?

A: Explanation is given below..

Q: Let A and B be m x n matrices and || || be any matrix norm for m x n matrices, prove that | || –…

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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: Let A = diagonalizable matrix( A = XDX-1), then X and D are: LO H O4

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Q: Find a diagonal matrix D and a nonsingular matrix P such that D= P-'BP.

A: A matrix is a mathematical object containing numbers arranged in rows and columns. The eigenvector…

Q: If A is an m X n matrix and B is an n x p matrix, matrix. To find in matrix A then AB is defined as…

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

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Q: If A is square matrix of order 3 such that|3 A| = 54. Find |A|

A: Using the properties of determinants

Q: Let A be a diagonalizable n x n matrix and let P be an invertible nx n matrix such that B = P-AP is…

A: Given Result: A be a diagonalizable n×n matrix and P be an invertible n×n matrix such that B=P-1AP…

Q: Let A and B be square matrices of order 3 such that |A-| = x + 7 with x + -7 and |A * A" | = . What…

A: A and B are square matrices. Therefore, det(AB)=det(A).det(B) det(A)=det((A)T) We will use these…

Q: Find a formula in terms of k for the entries of A, where A is the diagonalizable matrix below. 5-6 A…

A: Here we have to find a formula in terms of k for the entries of Ak, where A is the diagonizable…

Q: Let A be an m×n matrix, X an n×r matrix, and B an m × r matrix. Show that AX = B if and only if Axj…

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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: 1. Let A = [a)ax5, B = [bj]ax5, C = [cy]sx2, D = [dy]ax2, and E = [eg]sx4- Determine which of the…

A: We will answer the first three subparts of the first question as per our guideline. Please resubmit…

Q: Find if possible a nonsingular matrix P such that P-'AP is diagonal. 7 4 -4 (w) a-[] 1 2 (a) A (b)…

A: At first we find out eigen value of the given matrix. Then find out e vector.

Q: Let A be a nonsingular matrix. Show that A−1 is also nonsingular and (A−1)−1 = A.

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Q: Find a 3 x 3 matrix A such that A = 97 for all in R³. A =

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Q: Let A be the matrix Find p(A). p(x) = x' - 2r + 4

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Q: Let A be an m X n matrix with linearly independent columns and let A = QR be a QR factorization of…

A: Let A be an mxn matrix with linearly independent columns. The columns of matrix Q in QR…

Q: Let A be a nonsingular 4 x 4 matrix such that |A-1| = -2, then AT.adj(A-}) Select one: O True O…

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Q: Let A and B 5 Find the (1,2)-entry of matrix X 3 -3 given that AX+X=B. 9 3 -1 ||

A: follow netx step

Q: Find if possible a nonsingular matrix P such that P-'AP is diagonal. 7 4 -4 1 2 (a) A = 2 (b) А- -8…

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Q: O Let A be an m x n matrix, and let B be the result of performing a single elementary row operation…

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Q: Let A be an n xn matrix and B= A+1, where I is the identity matrix, then it is possible for A and B…

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Q: Let A be an n × n matrix and c a real number. Show that if cA = O , then c = 0 or A = O .

A: Given: A be an n × n matrix and c be a real number. To prove that: if cA=0 , then c=0 or A=0.

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: Let A be a nonsingular 4 x 4 matrix such that A = -2, then AT. adj(A) 4 Select one: O True O False.

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Q: Find all a and B >0 so that the matrix B = 23 6 2 is diagonally dominant;

A: A square matrix is diagonally dominant if   for .

Q: Let A = [a;;] be the n x n matrix defined by aji = k and a;; = 0 if i + j. Show that if B is any n x…

A: Given: A=aijn×n,     aii=k and aij=0 if i≠k. Let B be a square matrix of order 3 which can be…

Q: Let A, B, C be n × n matrices and assume that A is invertible. Solve the equation A(B + X) = C for…

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Q: Find matrix B such that AB = C. Hint: B = A^-1 x C *

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

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Q: Find x such that the matrix is singular.

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Q: Let A be a 4x4 matrix and det(A)=2. Find det(2A-)'

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

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Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.