Consider the following relationship: (x"A)~| = BC where A is a 2x3 matrix, B is a 3x3 matrix and C is a 3x2 matrix. What are the dimensions of X? 2x3 2x2 3x2 3x3 No such matrix X exists.

Q: Find two 3x3 invertible matrices A and B, such that A+B is not invertible.

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Q: • The Matrix B from 3 x 2 at by = 1- is 1. 3. 4. 1 -2

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Q: If the order of the matrix A is (3 x 5) and Bis (5 x 6) then the order of the matrix (A - B) will be

A:

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: Explain why the matrix A + C does not exist.

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Q: 32. Construct a nondiagonal 2 x 2 matrix that is diagonalizable but not invertible.

A: .

Q: Prove that the following is false by giving a counterexample. b c If matrix defis invertible, then…

A: consider the matrix of the form abcdefghi consider example 123484265 the inverse of the matrix…

Q: Let A be a 5x7 matrix, then the smallest possible dimension of Null(A) is:

A:

Q: Let A be a 4×5 matrix with 4 pivots. Do the columns of A span R4? Do they span R5? Justify your…

A: As A is a 4 x 5 matrix with 4 pivots so, it has a pivot in its every row. So, yes the columns of A…

Q: Suppose AB = I, . Show that the equation Bx=0 has only trivial solution. Explain why the matrix not…

A: Suppose that AB=In (then x n  identity matrix). The objective is to show that, the equation Bx=0…

Q: The nullspace of a 5 by 5 matrix contains only x = 0 when the matrix has ___ pivots. The column…

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Q: Let C be a 5 x 7 matrix with a rank 4. (1) What is the dimension of the solution space of Ax 0?

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Q: Explain why the columns of an n x n matrix A span R^n when A is invertible

A: From the given information:

Q: What scaling matrix S (in homogeneous coordinates, so 3 by 3) would produce a 1 by 1 square page…

A:

Q: If A is a 31x24 matrix whose rank equals 10, find dim(Nul(AT)). Your Answer:

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Q: If Ax = ax for nxn matrix A, nx1 matrix x, and a E R, determine a scalar 3 with the property that…

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Q: ve that for every matrix A, (AT)T = A

A: We have to prove that transpose of A transpose is A.

Q: I, explain why BTB must be symmetric for any n × m matrix B. (If yo

A: We will prove that the matrix Is symmetric as following.

Q: Suppose A is a 3xn matrix whose columns span R3. Explain how to construct an nx3 matrix D such that…

A: Please check step 2 for the solution.

Q: Give a 4 x 4 elementary matrix E which will carry out the row operation R2 + 4R1 → R2.

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Q: • Is it possible for a 5 x 5 matrix to be invertible when its columns do not span R°? Why or why…

A: According to the Invertible matrix theorem, the matrix with n x n order cannot be invertible if its…

Q: * Find the Matrix B from order 2 x 4 , Its elements are written in the form by = i + ()

A: Here we find matrix B of order 2×4

Q: 32. Construct a nondiagonal 2 × 2 matrix that is diagonalizable but not invertible.

A:

Q: Is there any 2x2 matrix with all non-zero entries, that is not diagonalizable but invertible? If…

A: Solution

Q: ind the 3x3 matrix that is equivalent in it's action to each of the

A: Given: To find 3×3 matrix that  equivalent to the symmetry operators are, a  S^2zb  C^2z

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: Find the matrix corresponding to the quadratic form Q(x) = x + 2x1x2 + 2x1x3. Is Q positive…

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Q: Suppose A is invertible and you exchange its first two rows to reach B. Is the new matrix B…

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

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Q: What is wrong with the following "proof" that every matrix with at least two rows is row equivalent…

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Q: Explain why the columns of an n×n matrix A span R^n when A is invertible.

A: Consider, a matrix A of order n, which is a invertible matrix.Since, the set of vectors

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: Suppose M is a (3x3) matrix such that the dimension of its column space is 2.Then the rank of M is…

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Q: If the null space of a 5 × 6 matrix A is 4-dimensional, what is the dimension of the column space of…

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Q: Find 6x6 matrix | a, that satisfies the stated condition. Make your answers as general as possible…

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Q: Explain transpose AT of the m x n matrix A?

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Q: If A is a square matrix whose rows add up to the zero vector, explain why A cannot be invertible.

A: Given A is square matrix whos rows add up to zero vector.

Q: Find 2x2 invertible matrices A and B such that A + B not equal to 0 and A + B is not invertible.

A: Wee need to find matrix A and B and do their addition and find invertible

Q: What is the rank of a 7x9 matrix whose null space is five dimensional? rank A =

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Q: Express the quadratic form as v Av, where A is a symmetric matrix. x² + 3y² + 5z² - 4xy+3yz + 10xz

A:

Q: Suppose a 6 x 8 matrix A has four pivot columns. What is the dim (Null A)? Is Col A = Rª ? Explain.

A: see below the answer

Q: Give an example of a 2 x 3 matrix A that is in RREF and whose solutions to 2 -(-) 4 Ax = 0 is…

A: Introduction: Systems of linear equations can be solved using a type of matrix called reduced row…

Q: Suppose that a l10 × 8 matrix A has 6 pivot columns. Then dim(ColA)- is Ą and dim(RowA)- is

A:

Q: Show that if a square matrix A has two equal columns, then A is not invertible.

A: since not a particular question asked ,as per guidelines solution to only first question (i.e Q1) is…

Q: Let A be a 5 × 4 matrix. Can the equation Ax=b be consistent for all b in ℝ5 ? Explain, please. Can…

A: Given that, A is a 5×4 matrix. Consider the equation, Ax=b. Here x is a 4×1 matrix with n=4 unknowns…

Q: Since it is, find the matrix P ^ -1 by using the adjoint matrix of the P matrix.

A: We are given that  We need to find the inverse of p-matrix

Q: Write down what it means for a n x k matrix to be singular.

A: As we know, If matrix is singular then it has determinant equals to '0' For Finding determinant…

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.