Let E be the elementary 3 x 3 matrix corresponding to the elementary row operation of multiplying Row 1 by -3 and adding it to Row 3. Show E is invertible.

Q: Suppose A = PRP–1, where P is orthogonal and R is upper triangular. Show that if A is symmetric,…

A: According to the given information suppose, It is required to show that if A is symmetric then R is…

Q: Find a 2 x 2 matrix A for which {;}. 5 E1 = span = span

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Q: Show that the matrix is not diagonalizable.

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

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Q: Let the matrix below be Anti-symr

A: Anti symmetric matrix is also known as skew symmetric matrix.

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

A: .

Q: If Q is an orthogonal matrix, prove that any matrix obtained by rearranging the rows of Q is also…

A: The matrix is said to be an orthogonal matrix if the product of a matrix and its transpose gives an…

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

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Q: The multiplicative identity matrix of order 3 is I3 =_______.

A: Let the Identity matrix be…

Q: If you know all 16 cofactors of a 4 by 4 invertible matrix A, how would you find A?

A: Given, an invertible square matrix A of order 4, and we know all the 16 cofactors of this matrix.…

Q: Consider an n x n matrix. Give 3 equivalent conditions for A to be invertible

A: Let A be an n×n matrix. we have to give 3 equivalent condition for A to be invertible. Conditions…

Q: Find an SVD of the indicated matrix.

A: The matrix is given of which SVD is to be calculated so,

Q: Prove that every skew-symmetric matrix of odd order has rank less than its order.

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Q: If A=XDX−1 where  X is a diagonalizing matrix of A, then 7X is also a diagonalizing matrix of A.…

A: Given: Where, X is a diagonal matrix of A, then 7X is also diagonalizing matrix of A. To determine:…

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

A:

Q: Let A be an m x n matrix with m>n.  Show that for any n x m matrix B, then AB does not equal Im. Use…

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Q: Find diagonal matrix D is similar with A a A =[? -5 And make sure can transtor diagomalizablewith

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Q: Let A be a 3x6 matrix of rank 3 then nullity of A equal 0 Select one: O True O False

A: From rank plus nulity theorem we know that : rank A + nullity A = the number of columns of A  From…

Q: Prove that an upper triangular n ×n matrix is invertible if and only if all its diagonal entries are…

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Q: If A is any 5 by 5 invertible matrix, then its column space is __ . Why?

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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: If A is a 6 × 8 matrix, what is the smallest possible dimension of Nul A?

A: Consider the provided matrix, Given, A is a 6 x 8 matrix. Since, the rank of A equals the number of…

Q: What does it mean to say that A is a matrix with dimensionm  n?

A: A matrix is a rectangular array of elements arranged in rows and columns. The size of the matrix is…

Q: Find the value of x so that the matrix is not invertible. 1. 3 2 0 [ 1 2 1 If answer is in decimal,…

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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: Let the n × n matrix A be equal to AT . Briefly describe the pattern of the entries in A.

A: Consider the matrix A of order n×n such that AT=A. let, A=a11a12…a1na21a22…a2n⋮⋮⋱⋮an1an2…ann  here…

Q: In the LU decomposition of the matrix if the diagonal elements of U are both 1, then the lower…

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Q: Let A and B be n x n matrices.  Suppose that AB = On where On is a zero matrix of size n x n, and A…

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Q: Find an invertible matrix P and a diagonal matrix D such that  P−1AP = D.

A: We need to find the matrix P and D.

Q: For a nonsingular matrix A and nonzero scalar k, show that (kA)-1 = A-1.

A: For a nonsingular matrix A and nonzero scalar K To show that kA-1=1kA-1 Consider a non singular…

Q: An n x n matrix A is invertible if ВА In АВ II

A: Inverse Matrix: Let A be an n × n matrix. If there exists an n × n matrix B such that AB = I = BA,…

Q: The multiplicative identity matrix of order 2 is I2 =_______.

A:

Q: Find a matrix P that diagonalizes 1 0 0

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Q: Is it true that when an n*n matrix whose columns form a basis of R^n, then A is invertible?

A: We shall answer this in next step

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: Let A be a nilpotent matrix of order n then A*n = 0 ) nxA = 0 A =nx1, l is Identity matrix

A: A be a nilpotent matrix of order n

Q: O Find the transforma tion matrix that wotates the axis X of a rec tangu lar coor dinale system 60…

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Q: Let A be a lower triangular n x n matrix with nonzero entries on the diagonal. Show that A is…

A: Consider A be a lower triangular matrix with non-zero entries on the diagonal.

Q: 2. Choose the rank of the matrix AT

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Q: Let A be an n × n matrixSuppose that the matrix C is obtained from A by interchanging the ith and…

A: Matrix C is obtained from A by interchanging the ith and jth row of A. We need to find an elementary…

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

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Q: Suppose that A is an n × n matrix satisfying the equation A4 + 2A2 − 3A − I = O , where I is the…

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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 an elementary matrix E that corresponds to the row operation of adding – 4 times Row 1 to Row…

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Q: Let A, be the n x n matrix each of whose entries is 1. Show that if n > 1, then In - An is…

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Q: If A is a skew-symmetric matrix then show that AAT = AT A and A² is symmetric. [Note AT denotes the…

A: We will use definition

Q: A matrix of order m x 1 is called a Choose.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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: Find an elementary matrix E that corresponds to the row operation of subtracting – 6 times Row 1…

A: Applying elementary row operation on identity matrix I we get the elementary matrix E.Now we find a…