suppose an nxn matrix has positive diagonal entries and negative everywhere else. suppose sum of the entries in each row are positve. prove det(A) is not 0.

Q: Suppose the trace of a matrix is equal to 10. If this matrix is also an identity matrix, how many…

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Q: Let Eki be the elementary matrix formed by subtractingα times the ith row of the identity matrixfrom…

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Q: Is the produ ct elementary. matri ces dalways OF two an swer. elementary ? Sustify your

A: The product of elementary matrices need not be an elementary matrix. Recall that any invertible…

Q: Show that a square matrix which has a row or a column consisting entirely of zeros must be singular.

A: Consider a square matrix A=000123456 and B=140250360 Here, all the elements of first row of the…

Q: Suppose that Q is an orthogonal matrix, then OaQ-8 ObQ-2 d 1Q-0

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Q: Put as many 1's as possible in a 4 by 8 reduced echelon matrix R so that the free columns are(a) 2,…

A: In a reduced echelon form of a matrix, if there is a pivot element in a row then, the elements above…

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: We call g(x1, x₂) = ax² + 2bx1x2 + cx a quadratic form, a, b, c are constants. Suppose X1 X = try to…

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Q: snip

A: The determinant of an orthogonal matrix is always one. Therefore to prove that the given matrix,…

Q: Place the smallest number of zeros in a 4 by 4 matrix that will guarantee det A = 0. Place as many…

A: In linear algebra, the determinant of a matrix is a scalar value that provides important information…

Q: Suppose that Q is 3 x 2 matrix with orthonormal columns then Oa Q'Q +1 Ob QQ" - I OcQ" - Q Od. Q"Q-…

A: The detailed solution along with the final answer is described below.

Q: Exercise 51. Is there a square matrix X with real entries such that det(X¹X) = -3?

A: detXTX=-3 X is a square matrix with real entries.

Q: If the nulI snace of a 30x17 matrix is 13-dimensional, find the rank of the matrix.

A: We have been given the matrix which is of 30 x 17 i.e it has 30 rows and 17 columns. And it is also…

Q: Suppose A is a square matrix. Show (a) A+A" is symmetric, (b) A – A" is skew-symmetric, (c) A= B+ C,…

A: Sum of symmetric and skew-symmetric matrix is matrix it self. Like for matrix A, Symmetric matrix =…

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: Show that the matrix; is singular

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Q: Enter a 3 x 3 symmetric matrix A that has entries a1 = 1, a2 = 5, a33 = 4, a12 = 0, a31 = 3, and a A…

A: A square matrix A is called a symmetric matrix if A=AT, i.e. a matrix is equal to it's transpose If…

Q: & Gier, Mamiten 3. - 2 -4 -6 12 15 3 -12 3 ID 2. ーC 4 6. 4 15 4x 5 5x3 No.of Column A No.of mws in B…

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Q: Suppose A is nxn matrix and the wquation Ax=0 has only the trivial solution. Explain why A has n…

A: If the equation Ax=0 for an n×n matrix A has only a trivial solution, it implies two key things…

Q: 2 0 -1 1 -2 2 A = 2 -1 0 1 -1 6. ||

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Q: (a) Show that the jth column of the matrix product AB is equal to the matrix product Ab;, where b;…

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Q: Select all of the following that are true for all nxn matrices A and B. AA²-A²A (A+BILA-B)-A²-B²…

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Q: If xER" is a column vector (i.e. an n ×1 matrix), then In-2xx' is always a symmetric matrix. True…

A: Consider the given column matrix as x=x1x2⋮⋮xn-1xn, x∈Rn. Compute the transpose of the matrix x as…

Q: Prove that a 2×2 matrix transforms any straight line into a second straight line and points on the…

A: Let the 2×2 matrix be A=a11a12a21a22 which is the matrix of a linear transformation T:ℝ2→ℝ2. Let the…

Q: Please compute the next matrix

A: The solution is provided for A. We shall solve B and C.

Q: Prove or disprove: If the columns of a square n ×n matrix M are linearly independent, so are the…

A: Linearly independent and dependent vectors

Q: Suppose A,B,C are each nxn invertible matrices. Show (ABC) CBA.

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Q: o matrices A and B one has that Null(B) is contained in Null(A · B).

A: Given, for two matrices A and B, to show that Null (B) contained in Null(A·B).