If A is a matrix of order 3 x 6, Bis a matrix of order 6 x 4, then the product of order AB is ? 1) 6 x 4 2) 3 x 4 3) 3 x 12 4) 6 x 8 5) 6 x 12

Q: Given that G is a 1 × 6 matrix and H is a 6 × 1 matrix, a. Is GH defined? If so, what is the order…

A: Given that G is a 1 × 6 matrix and H is a 6 × 1 matrix,a. Is GH defined? If so, what is the order of…

Q: Construct a 3 x 3 triangular matrix A so that 1] the vector 2 is in Col A. 3]

A: We know every lower or upper traingular matrix is a triangular matrix.

Q: Prove that if B is the matrix obtained by interchanging the rows of a 2 ×2 matrix A, then det(B) =…

A: Let the matrix A and the new matrix B be as follows.

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: , Does there exist an 8 x 8 matrix A = (as) satisfying the following three conditions? (i) If i 2 j…

A:

Q: Let A, B & Mn (C) be Hermitian matrices. Then

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Q: if A is (m*n) matrix, prove 'rank(A)=n-dim(N(A))

A:

Q: Let A be an 3 x 4 matrix. What must c and d be if we define the linear transfor- mation T: R → Rd by…

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: snip

A: Given, A=abcdD=ad-bc≠0

Q: Given the partitioned matrix A = [ B]. B]₁ C D in which B and C are invertible. Which of the…

A:

Q: 2. Show that if A is an n x n real symmetric matrix then (Ax) y = x (Ay) for all x, y E R".

A:

Q: Prove the given theorem: For any square matrix A with real number entries, A + A′ is a…

A: Given: Prove that for any square matrix A with real number entries, A + A′ is a symmetricmatrix and…

Q: Prove that if A is an n X n matrix, then A - Ar is skew-symmetric

A:

Q: where En is a k-dimensional vector, A e Ckxk is a constant matrix, and B : Z+ Ckxk is a matrix…

A: Given,      tn+1-t¯=∑i=01αi(tn-i-t¯)+∑i=01βi(zn-i-z¯)…

Q: Is it true or false? If A is nxn matrix, c is scalar, then cA |=c | A| Birini seçin:

A:

Q: Consider A and B are two square matrices and B is a scalar. Calculate (BA^T B)^(-1) = *

A:

Q: Find a 2 x 2 matrix B + 0 and B + 1, such that AB = BA, where A How many such matri- 2 ces B are…

A: Given data: The matrix is given by "A". A=1221 Consider the matrix "B". B=abcd According to the…

Q: Suppose that A and B are matrices having n rows. Prove that M(A|B) = (MA|MB) for any m ×n matrix M.

A:

Q: Suppose B = QRQ-1, where Q is orthogonal, and R is upper triangular. Show that if B is symmetric,…

A: Given that B=QRQ-1 where, Q is orthogonal and R is upper triangular. Then, multiply Q on both sides:…

Q: Given a 3x matrix in terms of scalar c and that det (A)=8, find the valuddof G if -1 1c-2 C+7 3. 2.

A:

Q: Let A and B be n × n matrices such that AB is invertible. Show that A must be invertible. You cannot…

A:

Q: Consider the multiplication AB is existing with the size (M × N) , where B is a matrix of size (L ×…

A: Consider the given information. The multiplication of two matrix is possible if and only if the…

Q: Prove that B is row equivalent to A if and only if there exists a nonsingular matrix M such that B =…

A:

Q: Prove that for any matrix A ∈ Mm×n(F), (R(LA∗))⊥= N(LA).

A: The objective is to prove that

Q: Г1 3 2 5 1 [3 4 2

A:

Q: (i) Use the properties of trace to argue that tr(AʼA) = tr(AA') for any n × m matrix A. [2 0 (ii)…

A:

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

A: Using the properties of determinants

Q: Find a matrix B such that AB = I, where [ ] 8 1 1 0 A = and I = -8 8 0 1 1 a b Hint: Let B = %3D c d…

A:

Q: Find the LU tactorization of 2 -4' -4 7 10 18 That is, write A = LU where L is a lower triangular…

A: I have used Gauss elimination method to find LU decomposition

Q: let B- 8. find a triangel ar matrix A such that

A: A triangular matrix is a type of square matrix. These are of two types:  Lower triangular  upper…

Q: If a matrix A E Mn(R) and rank(A) = n, is it true that the column vectors of A are linearly…

A:

Q: Suppose A is rectangular ( m by n) and S is symmetric ( m by m).(a) Transpose AT SA to show its…

A: Given: Matrix A is rectangular ( m by n) and matrix S is symmetric ( m by m).

Q: Let A € RPXm have rank r. Show that there are matrices C and B such that A = св, where C E RPXT and…

A: Please check the solution in next step

Q: Use the Cayley-Hamilton theorem to find A1, A°, and A“ for the given matrix A. 1 5 1 A = 0 2 1 0 0 2

A:

Q: Show that if A is an n x n symmetric matrix, then |(Ax)•y = x•(Ay) for all x, y in R".

A: In symmetric matrix, transpose of the matrix is equal to the matrix. AT=A

Q: Given C and D are matrixes, and their products CD and DC exist, what can we tell about their…

A: Matrix multiplication is the process of multiplying two matrices using dot product. Dimension of a…

Q: Let A € RPXm have rank r. Show that there are matrices C and B such that A = CB, where C e RPxr and…

A:

Q: Suppose A is a 2 x 2 matrix such that for all x, y E R², (Ax) · (Ay) = x ·y Must it be true that A…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Assume A and B are two m × n matrices with the same reduced echelon form. Show that there exists an…

A: Given A and B are two m×n matrices with the same reduced echelon form. We have to show that there…

Q: Explain why the columns of an nxn matrix A span R" when A is invertible. Choose the correct answer…

A:

Q: Determine the matrix C such that (CT – 21) 1 1 2 2 3

A:

Q: Prove the corollary to Theorem 3.16: The reduced row echelon form ofa matrix is unique.

A: Given: Theorem: The reduced row echelon form of a matrix is unique.

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…

A:

Q: If U is a square matrix such that UTU I, what can we say about det (U)?

A:

Q: Suppose A is a matrix of order p × q and B is a matrix of order q × r, then illustrate the order of…

A:

Q: let A be an mxn matrix and v and w vectors in Rn. If v and w were both solutions to Ax=0, show that…

A:

Q: If the n x n matrices A and B are orthogonal, which of the matrices in Exercises 5 through 11 must…

A: Given- A and B are n×n orthogonal matrices. To find- A+B is orthogonal or not?     Concept Used-…

Q: For A e Mnxn(C), the function ||A||. = max1<ijśn |aij| is a norm on Mnxn(C) but not a matrix norm.…

A: Matrix Norm: Let Mn×n(ℂ) be the vector space of all matrices of order n with entries in the field ℂ,…

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.