T1. It can be proved that a nonzero matrix A has rank k if and only if some k x k submatrix has a nonzero determinant and all square submatrices of larger size have determinant zero. Use this fact to find the rank of [3 -1 3 2 51 5 -3 2 3 4 A = 1 -5 0 -7 -3 7 -5 1 4 1 Check your result by computing the rank of A in a different way.

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A: We know that an m×n matrix has m rows and n columns and if m=n then, the matrix is said to be a…

Q: Suppose that an n× n matrix A has a QR-decomposition where 1 -2 0 0 R = 0 1_1 0 -2 What is the…

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Q: 3. State the appropriate theorems that justifies the given equality. 3 2 1 2 6 8-4 5 3 = = 0 4.…

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Q: Compute the determinant of the matrix A, below, by using row operations to transform A to an…

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Q: -1 004 -1 1 04 1 -2 0 3 2 0 -3 -2

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Q: |2 2 x| 1. Find x, if 3 3 3= 24 4 x 4

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Q: 4. Determine whether the given matrix is invertible without computing its determinant. -3 0 1 3 5 8…

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Q: Identify all of the true statements below about elementary matrices. Any elementary matrix that adds…

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Q: Let A, B and C be three n x n invertible matrices with A² = A. Solve the following matrix equation…

A: Given ,  are three  invertible matrices with    .And    Since  are invertible matrices, exist  .

Q: Consider a 20x20 invertible matrix A whose determinant is 2. Let B be the matrix obtained from A by…

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Q: Show that every 2 x 2 matrix A of determinant 1 is the product of three elementary matrices. This…

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Q: Example: Find a basis for the null space of the matrix -3 1 2 -1 1 0 0 -1 0

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Q: 2. Let A be any 4 × 4 matrix with determinant -2. (a) Let N be the matrix obtained from A by…

A: Given, |A|=-2(a)Matrix N obtained from A replaced R1 by -4R1Here scalar=-4∴…

Q: II. Find the determinant of the following matrices by row reduction: [1 1 1 11 a 1 1 11 1 3 3 3 3 1…

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Q: 1 be the n x n matrix with the following form: 1 1 1 1 1 .. 1 2 2 2 ... 1 2 3 3 3 ... A = 1 2 3 4 4…

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Q: Suppose that A and B are n x n matrices, where B is nonsingular. Prove that the determinant of BAB-¹…

A: We use properties of determinant.

Q: [A]-and (8) [: and (C]- then find (A +(8]C]

A: see below the answer

Q: Find the determinant of the following matrix using elementary row operation [1 2 2 A= |1 10 2 4 4 Is…

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Q: -1 9. 1 8

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Q: III. Find all the values of the variables in the following matrices that will make its determinant…

A: Here we have find the values of the variables in which the given matrix that will makes its…

Q: 2. Calculate the product of each pair of the following determinants, using Property 12, and check…

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Q: (1 2 3 4) 4 1 2 3 3 4 1 2 3 4 1 and four to row one (and explain why this does not change the…

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Q: Let A be any 4 ×4 matrix. Compute the determinant of the appropriate elementary matrix to prove each…

A: consider matrix A of 4x4 order.

Q: 2. Compute the determinant of the following matrix [1 0 0 31 0 2 1 0 0 1 2 0 3 0 0 1] A = 3. Compute…

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Q: Let Ao be an 5 x 5-matrix with det (40) = 3. Compute the determinant of the matrices A1, A2, A3, A4…

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Q: Can we use cofactor expansion in a 2 x 2 matrix? What is the determinant of a 1x 1 matrix?

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