Suppose that A = a a 1 1 b 1 2 B = 300 000 0 00 and A and B are similar. (1) Calculate a and b; (2) Find a nonsingular (invertible) matrix P such that P-¹AP = B.

Q: Let A = 2 1 54 Write 5A. Is det(5A) equal to 5det(A)? 5A= (Type an integer or decimal for each…

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Q: Select all statements below which are true for all invertible n x n matrices A and B DA. (A+ A-1)6 =…

A: A) Apply binomial theorem for LHS.…

Q: Find a matrix A such that 5 ¹0-08-08-0 A 5 A A = A =

A: We can solve this as follows:

Q: 3) Consider the following matrix: A= 220 001 0 10 - 1 1 (i) Compute A™ ¹. (ii) Write A as a product…

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Q: Show that any 3 × 3 matrix of the form ⎧ ⎩ a 1 0 0 a 1 0 0 b ⎫ ⎭ is defective.

A: We have to show that given matrix is defective.

Q: Construct a 3 x 3 nonzero matrix A such that the vector 1 is a solution of Ax = 0. 1 A =

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Q: Suppose matrix A as follows: 2 -17 3 -2 0 ^ = [2 -1 a. Find the eigenvalues and eigenvectors of the…

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Q: Suppose A is a 2 × 2 matrix. Use the characteristic equation to show that A and A¹ have the same…

A: We have to show that  have same eigenvalues using given data.Concept required:Eigenvalues of are…

Q: Find all matrices B that commute with 1 + i (¹+1) :). 0 A = That is, for which AB = BA.

A: Let B=abcd be the matrix such tghat AB=BA

Q: Find a 3 x 3 matrix A such that Az = 10 for all i in R³. A =

A: Given Ax=10x  We have to find 3×3 matrix A  Now

Q: Let A and C be n×n matrices such that ​CA=I​ (the n×n identity​ matrix). Show that Ax​=0 has only…

A: Here, CA=I, where I is the identity matrix.

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: Find the power of A for the matrixA16

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Q: Suppose A is an n×n invertible matrix such that A – 2A = I, . Find an for A. expression

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Q: Find a 3 x 3 matrix A such that A A A A = 1 4 0 = 2 0 -1 B-B EL. 0 2 1 = -3 and 0 -5 0 -5 B-B 0 -5 1…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: a) Suppose that A and B are 4 x 4 matrices, det(A) = 2 and det((3ATB)-¹) = . Calculate det(B). b)…

A: As per our company guideline we are supposed to answer only one question kindly post remaining…

Q: Find the matrix B such that 2AT+3B=0.

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Q: Consider the matrix 1 0 2 ^-(4) A = 0 -1 -1 1 1 -2 Calclulate A³ A, deduce that A is invertible and…

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Q: Find matrix D such that D=2A+B-C

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Q: Suppose A, B, and X are invertible 3 x 3 matrices. Suppose that [1 2 0 0 1 1 1 3 • A8 = I3; and…

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Q: For nxn matrices A and B with B invertible AB and BA have the same eigenvalues. Select one: O True O…

A: The eigenvalues of product of two n*n square matrices will have same Eigen values.

Q: 3. Determine the last column so that the resulting matrix is an orthogonal matrix: 1/√2 1/√2 0 1/√6…

A: The given matrix is .To determine the elements of the last column so that the matrix is orthogonal.