Given a 2 by 2 matrix, how do i show that it is a linear combination of unitary matrices

Q: Due to what property, applied to the matrices below, do we know that A + (−A) = O?

A: A+-A=O

Q: If A and B are sk ew-symmetric 2 X 2 matrices, under what conditions is AB skew-symmetric?

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Q: Diagonalize the matrix 1 0 -1 A = -2 3 -1 -2 0 2 In other words, you need to find a diagonal matrix…

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Q: If A is a 5 x 6 matrix and the sum A + B can be computed, what is the size of B?

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Q: If A is an 3× 4 matrix and the nullity of A equals 2, find the rank of A .

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Q: find an LU factorization of the given matrix.

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Q: Find a sequence of elementary matrices whose product is the given nonsingular matrix.

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Q: Due to what property, applied to the matrices below, do we know that A + B = B + A?

A: Due to Commutative Property Of Addition of matrices, we can say that: A+B=B+A. Where, A,B,C are…

Q: Suppose A is a symmetric nxn matrix and B is any nxm matrix Show that B'AB, B'B, and BB' are…

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Q: of a matrix is the factorization of a given square matrix into two triangular matrices.

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Q: Suppose A is a 5 x 5 nonsingular matrix, and Bis the result of exchanging the second and fourth rows…

A: If a matrix A is non-singular then all the rows and all the columns  of A are linearly independent.

Q: TRUE OR FALSE. The product of two m × n matrices is defined.

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Q: 3. If A, B and C are matrices with orders, 3 X 3, 2 X 3 and 4 X 2, respectively, which of the…

A: Note: There are many subparts in the question. So I will answer the first three subparts.…

Q: 6. If A is a 4 x 2 matrix and B is a 3 x 2 matrix, what is the size of ABT?

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Q: . With numbers, a∙b=b∙a and we say that multiplication is commutative.  Is matrix  multiplication…

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Q: Given two matrices A and B, how can you determine the order of AB, assuming that the product is…

A: Let order of A is mxnAnd let order of B is nxp (because product of AB is defined)

Q: Let A be an mtimes×n matrix and let B be an ntimes×p matrix. If the first row of A consists only of​…

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Q: If A is a 2 x 3 matrix and the sum A + B can be computed, what is the size of B?

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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: What is the possible operation to reduce matrix A to an identity matrix using elementary row…

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Q: What is trace of matrix (2A+3B)

A: Find the trace of the matrix(2A+3B)

Q: If A and B are row-equivalent matrices, then they must have the same rank. True False

A: Our guidelines for multiple questions, answer only first question  Answer = (8)  If matrices "A"…

Q: Let A, B, and C be invertible matrices. Then (4A-1B"C²)-1 is equal to c--(B")-1A equal to the above…

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Q: When two m x n matrices are said to be equal? Explain there Applicability?

A: Two mxn matrices are said to be equal if their corresponding elements are equal.

Q: Given A = 1 1 0 3 Compute 5A *Matrix

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Q: The sum of two skew-symmetric matrices is symmetric. Select one: True False

A: Solution in step 2

Q: 4. A matrix A is similar to matrix B, if for some invertible matrix P, B = P'AP. Is B similar to A?

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Q: If A is an invertible square matrix that is row equivalent to matrix B , then both A and B are row…

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Q: The order of the single matrix obtained from 1 1 -1 To 1 23 is 1 0 21 -1 0 2 2 0 3 2 (a) 2 x 3

A: Here the order of the matrix needs to find out for both terms. Subtraction and addition won't affect…

Q: What is the linear combination of the matrices аnd

A: The explanation are as follows

Q: In general, it is difficult to show that two matrices are similar.However, if two similar matrices…

A: Given two n × n matrices, A and B, we say that A is similar to B if there exists an invertible n × n…

Q: True or False If A and B are n × n lower triangular matrices, then AB is also lower triangular

A: Given, A and B are n×n lower triangular matrices. Consider 2×2 lower triangular matrix A=a0bc…

Q: For skew anti-symmetric matrix, the sum of its entries is (A 1 В -5 10 E -1

A: We want to find sum of entries of skew anti-symmetric matrix.

Q: If A is 3 x 2 matrix and B is 2 x 3 matrix, then AB is always: a. Invertible matrix b. singular…

A: We know that rank ofAB is always less then or equal to min{rank(A), rank(B) }

Q: Given that A is a 4 × 2 matrix and B is a 2 × 1 matrix, a. Is AB defined? If so, what is the order…

A: a) A is a 4 × 2 matrix and B is a 2 × 1 matrix Since number of coulmns of A=number of rows of BSo AB…

Q: Suppose that A is a 3×3 matrix and det (A) = -4. What is det (4A)?

A: By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Q: For a square matrix A, AAT = ATA. %3D A) True False

A: We have to find the given statement is true or false.

Q: I. State whether or not the given matrix is (a) upper triangular, (b) lower triangular, (c)…

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Q: If A and B are nXn matrices, then (AB)²=A²B? A True

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Q: Find 2x2 matrices, A and B, such that AB = 0, but BA is NOT EQUAL to 0.

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Q: . We can add (or subtract) two matrices only if they have thesame .

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Q: If the __________ of a matrix is p× q, then p represents the number of __________ and q represents…

A: If the order of a matrix is p x q, then p represents the number of rows and q represents the number…

Q: Given that A is a 1 x 7 matrix and B is a 5 x 1 matrix. (a) Is AB defined? If so, what is the order…

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Q: If A and B are invertible 2 × 2 matrices with nonnegative entries, then A + B must also be…

A: Let's take one counter example of the given conditions. That is A and B are invertible 2*2 matrices…

Q: If A is a 6×1 matrix and the sum A+B can be computed, what is the size of B?

A: Matrix addition. If A and B are matrices of the same size, then they can be added. (This is similar…

Q: If A is a 3x5 matrix, what is the largest possible value for its Rank? O 3

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Q: Consider matrix A. -3 52 A= 8. -1 3 What matrix results from -8-A?

A: Given that: A=-3528-13

Q: Suppose A is a 3 x 4 matrix. If we can successfully multiply A with the matrix B, then which of the…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.