6.* Suppose that A = [aj] is a 3 x 3 matrix whose entries are equal to either 0, 1, or 2, namely aij e {0,1, 2} for every i, j e {1,2, 3}. Suppose that A is invertible, and write A- = [b;]. Explain why, for i,je {1,2,3}, b;j is a rational number of the form k/2' or –k/2' for some positive integers k, l (depending on i, j).

Q: 8.Find the inverse of the given matrix -3 7 4 -7 3 -6] 1 A = -1 -1 -3 A) A¹ = 0 0 1 B)A-¹ = C) A-¹ =…

A: I have given the answer in the next step. Hope you understand that

Q: 7. Compute A100 where A = -5 6 3 -2 Find a matrix B such that B³ = A.

A:

Q: Let A be an 7 × 7 matrix in which every entry is 1 and I7 be the 7 × 7 identity matrix. Prove that…

A: Matrix 'A' is  defined such a way that , all the entries are 1 of order 7×7. Some results: If sum…

Q: 7. Let A, B and C be n x n matrices and let D = ABC. Prove that if D is nonsingular, then A, B and C…

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Q: If AT + B = C, what is A?

A:

Q: 10. Suppose that A is an n x n matrix with real entries such that the diagonal elements are all…

A: The problems with proof can be solved by using the concepts in linear algebra. A diagonally dominant…

Q: 5. Find the three by three matrix A such that [r – y] A. y for all r, y, z in R.

A: In the given problem we have to find the three by three matrix A such that…

Q: 7. Let A be an invertible matrix. Prove that if A-¹ = AT, then det(A) = +1.

A: Given: A is an invertible matrix. If A-1=AT, to prove that detA=±1

Q: Consider the nxn Hilbert matrix defined by 1 H = 1 13 1 n n+1 1 3 1 4 1-n 1 n+1 n+2 1 n+2 1 2n-1…

A: The answer is hij=1i+j-1

Q: Given that P and O are 3 x 3 invertible matrices then (A-"B) = A. AB-! B. B-'A C. B-'A-! D. BA-

A: Given : A-1B-1

Q: rix with even mumber of permuta Q4. If all elements of A and A are integer numbers, what are the…

A: Let A be any n×n Matrix with integer entries

Q: find the twelfth pawer X of the matrix X that satusfies the Equation 12 X A = AD

A: XA=AD⇒X=ADA-1⇒X12=ADA-112=ADA-1·ADA-1·…·ADA-1=ADA-1ADA-1A·…·A-1ADA-1=AD12A-1

Q: 4. Find the null space and column space of the matrices 0 1 1 -2 1 1 0 1 22-4 0 -1 0 1 -3 A = 1 2 3…

A:

Q: 5) A matrix A is diagonal if A¡j = 0 for i + j. Entries on the diagonal are not required to be…

A:

Q: 4. Let A be a square matrix with transpose A". • If AT = A, then A is called a symmetric matrix. %3D…

A: If A is non singular then A is non zero. ATT = A

Q: Let a matrix '2 -2 1 A 2 3 1 1 -2 - 2 2 Show that A"A = I and deduce that AT = A-1.

A:

Q: 6. Given real m×n matrix A, real nxp matrix B and real number c, prove: c(AB)= (cA)B

A: The product of matrix A and matrix B is possible because the number of columns in matrix A is equal…

Q: Invert the following matrix Зх — 2у — 9 -x + 3y = 3

A:

Q: 1. Let D = the sales of DVDs in billions of dollars, S = the total sales of streaming videos in…

A: The sales of dvds given as the function D = -0.92t + 8.75 and the total sales of streaming videos…

Q: = (3, 6) 2. It is known that u = (-2,3) and v = relative to the inner product in R? which is derived…

A: 2 Given that u=−2,3 and v=3,6 And A=2134. We have to find the u and v. We know that…

Q: 9. Let A be an n x n matrix in reduced row echelon form. , then A has a row consisting entirely…

A:

Q: 4. Suppose A is a nonsingular matrix with SVD A= UEV*.

A:

Q: 7. Let M be a 3 × 3 matrix. Prove that if M is upper triangular or lower triangular, then det (M) is…

A:

Q: 3.) Let Find A1 A- 203 010 100 using confactor representation of the imorse matrixe

A: The given problem is to find the inverse of the given matrix by using the cofactor representation of…

Q: 27. Let A be square n x n-matrix. Show that A + AT is symmetric. Show that A+ ATY X. Ax = x X for…

A: Given  is a square matrix of order  .To show that matrix  is a symmetric matrix.And to show  for all…

Q: Let A AX Solution. Let X ΧΑ X₂ = = X3 = - (1 2²0) 1 0 6 2 -4 x+20*Z = 4*x+Z x+4*y 4*t+z 5 10 Find…

A:

Q: 7. Let A be an 7 × 7 matrix in which every entry is 1 and I, be the 7 × 7 identity matrix. Prove…

A:

Q: 4. Suppose B, I – B-' are invertible matrices and (X – A)- = BX-1, find X (as an expression in A,…

A: A matrix Y is said to be invertible if and only if Y-1 Y=Y Y-1=I

Q: 3 12. Let A -2 1 Compute the matrix-vector products Au and 34 Av and compare them with b. Is it…

A:

Q: .3.5. For n×n matrices A and B, explain why each of the following in- equalities is valid. (a) trace…

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Q: A. modrix g 1 - V fo " Kariky hdher de matrix の det A- 2.

A: For part (i) of a: According to the given information, it is required to calculate the determinant…

Q: Find the characteristic equation for the matrix A 3 0 0 A = 0 1 -1 0. 1 3 -X3 – 7X? – 16X + 12 = 0…

A: Use the method of characteristic equation to find it as in next step.

Q: Prove that the product of two n x n anti-diagonal matrices is diagonal.

A: To prove that the product of two n*n anti-diagonal matrices is a diagonal matrix.

Q: 4. Let martix A is any (mxn) matrix and let B is a square matrix. Show that, any vector 'b' chosen…

A: Given: Matrix A is (MxN) Matrix B is square and diagonal matrix Vector B is coloumn space of matrix…

Q: 7. Suppose U is an m x n matrix and V is an n x m matrix for which In-VU is invertible. Show that…

A:

Q: 13. a) Show that if A and B are n x n matrices, at least one of which is invertible, then AB and BA…

A: (a) If A and B are two n×n matrices, and one of them is invertible, then show that AB and BA are…

Q: 7. For 13 i33 and 1s j<3, let aij denote the element in the ith row and jth column of a matrix A.…

A:

Q: 2 Be A, a square matrix i. Given that A holds = 44 + 5I . Prove that A is reversible, and express A-…

A:

Q: Let matrix A be 2 by 2 matrix and 1 A. 4 and 1 4 .2) 2 Then what is A=? ||

A: At first we will suppose a matrix A as 2x2 matrix and simplfy second condition by pre multiply by A…

Q: 3. Suppose A is an n x n matrix such that A³-3A² +21= Onn. Show that A is invertible and find its…

A: