[1 -2 -1] with |4|=-7. Let A= 0 1 |3 -1 0 Matrix B is obtained by modifying matrix A, with B+ A. Write down a matrix B, and explain how it was obtained so that: |B|=7 |B|= -7 |B|=-14 |B| = 0 . 2 a) b) c) d)

Q: Show that there is no matrix A E M250x250 with real entries satisfying AAT = -I.

A: Given that A is real ( All entries are real)  square matrix of order 250×250. The trace of any real…

Q: 4. If det(Adj(A)) = then what is det (A-1) if A is a (4 × 4) matrix?

A:

Q: If a 6 x 3 matrix A has rank 3, find dim Nul A, dim Row A, and rank AT .

A: We are given that a 6x3 matrix A has rank 3. So, dim(Row A) = 3. We know that dim(A) = dim(Row A) +…

Q: If A * I = A, and A is a 3x5 matrix, what are the dimensions of I? Show complete solution as proof.

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Q: 2 Construct a 3 by 3 nonzero matrix A so that vector is a solution to Ax = 0 -

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Q: 2) An n x n matrix A is called nilpotent if Ak = 0 for some positive integer k. Show that if A + 0…

A:

Q: Given that A, B, C are all square matrices of the same size, matrices A and C are both orthonormal,…

A:

Q: Let 2 -1 | -1 2 -1 -1 -1 -1 -1 –1 -1 2 -1 2 be the Eç Cartan matrix corresponding to the simple…

A:

Q: 4. Prove: If b is a non-zero vector, and x and x are both solutions to the matrix equation AX =6,…

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: Find 6×6 matrix a, that satisfies the stated condition. Make your answers as general as possible by…

A: Let the genral 6*6 matrix is given by…

Q: Express the following matrix as a product of several elemen- tary matrices. 1 3 E 2 3 ||

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Q: 4. Prove that det (A) = det (A¹) for a 2 × 2 matrix.

A:

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

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Q: Consider the matrix. P = in order 4, where X1, X2, X3 and X4 are the matrix x4 rows of P. If we have…

A:

Q: Suppose that A+ is a 2 × 2 matrix and that A+ = -A. Show 7.2 that iA is awesome.

A:

Q: 4. Decide if there is a three by three matrix A such that A. 1 for all æ, y, z in R.

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Q: If A and B are square matrices of the same size such that AB = BA, prove that (AB)2 = A2B2.  By…

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Q: What is the only 3x3 matrix B such that for every 3x3 matrix A, ВА — 2A? What is the only 3x3 matrix…

A:

Q: Show that A = P-¹BP. [2-13] -4 and B = 1 -2 -2 2 are similar matrices by finding an invertible…

A: To show that          A=7-132-4, and   B=1-2-22 are similiar matrices.

Q: Find a 3 x 1 matrix x with entries not all zero such that 1 2 -1 Ax = 1x, where A 1 1 -4

A: A=1  2-11  0  14-4  5 Now let x=abc be the required matrix. Now consider, Ax=1x⇒1  2-11  0  14-4…

Q: 2) If IAI = 3, where A is a 3x3 matrix, caleulate the folowing: 2a) det ( ZA) 26) det (A) 2c) det (…

A:

Q: Prove that the quadratic equation A^2 - 3A = 2I hold true for the matrix A =  5  -6  -6        -1…

A: The detailed solution is as follows below:

Q: g.... r, be vectors in R", and let Q be an mxn matrix. Write the matrix Qr, Qr, as a product of two…

A:

Q: 2. Assuming that all matrices are nxn and invertible, solve for D. CTB-A'BACDA²²B™C-2 = CT

A: We use properties of invertible matrices.

Q: 2.4 Use this matrix N to rotate the point (0, 3) an angle of 180° anticlockwise around the point (1,…

A:

Q: 31. Let A be a 5 ×7 matrix with rank 4. a. What is the dimension of the solution space of Ax = 0? b.…

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Q: Illustrate the Gersgorin theorem by the matrix 2 1+ 2i 0 A = -1 -2 – 2i 1/4 1/41/2 140 12 1/7 1/2…

A: We state the theorem and explain it with the help of the given matrix A.

Q: Assuming that all matrices aren xnand invertible, solve for D. BCA DCB'A = BC?.

A: Properties of invertible matrix:  If a matrix A is invertible and then there must exist a matrix…

Q: Use Proposition 2.50 to state Jacobi's method and the Gauss-Seidel method in matrix notation for the…

A:

Q: FIND THE FUNDAMENTAL MATRIX AS W ELL AS THE FUNDAMENTAL MATRIX SATISFYING )- I x'= -4 %3D

A: For the solution follow the next steps.

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: such that the vector 2 is a solution of 13. Construct a 3 x 3 nonzero matrix Ax = 0 123

A: I have construct a block matrix

Q: 6) Find the SVD of the matrix by manually calculating U 4 11 14 A = 8 7 -2]

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Q: Prove that ||A||₁, ||A||, || A||₂, are matrix norms.

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Q: 7. Show that the matrix A=I– 2vv' , where v is a unit vector in R", and I is an nxn identity matrix,…

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Q: We will define a checkerboard matrix to be a square matrix A = (aj), where if i + j is even if i +…

A: For row reduced form of nxn checkerboard matrix contains 2 non zero rows only. So the rank is 2 (…

Q: 3 3 , Let M 1 -2 -3 Find c1, C2, and C3 such that M3 +¢¸M² + c2M + C3I3 = 0, where Iz is the…

A:

Q: Consider the following matrix. Find the proper procedure for changing the ements to zero. 1 1 - 1 -5…

A:

Q: are the two matrices Simi Siari? If So find B=P'AP 20 030 3 00 A=

A: The solution are next step

Q: Find a basis for the nullspace of the matrix. (If there is no basis, enter NONE in any single celI.)…

A:

Q: 5. Show that if M is a 3 x 3 magic square with weight w, then we can write M as M = Mo+ kJ where Mo…

A: M is a 3 x 3 magic square matrix with weight w. We take weight, w=15 The matrix of M is  Add any…

Q: Suppose that A and B are square matrices with the property AB = BA. Show that ABn = BnA for every…

A:

Q: DHI Reduce each Hhe following matriceg Into Me of indicated form. (i):- -2 3-ノ red uced eehelom fom.…

A: Solve the given problem.

Q: If a 6 × 3 matrix A has rank 3, find dim Nul A, dim Row A, and rank AT

A:

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

A:

Q: Find a basis for the nullspace of the matrix. (If there is no basis, enter NONE in any single celI.)…

A: The given matrix is A=15-2401-12-2-104-8

Q: Prove that A4, A||, ||A||₂ are matrix norms.

A: Given: ∥A∥1, ∥A∥∞, ∥A∥2 To prove ∥A∥1, ∥A∥∞, ∥A∥2 are matrix norms.

Q: For matrices M and N, the 3rd column of NM is all zeros. Matrix M has 5 columns and none of them are…

A: Please find the detailed solution in next steps

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.