Let -5 -0.5] 1.5 -3 Find an invertible matrix S and a diagonal matrix D such that S-¹AS = D. A = -188 S= D=

Q: Write B as a linear combination of the other matrices, if possible. (If not, enter DNE in all…

A: We will find the required.

Q: Let A be an invertible 3 by 3 matrix. Assume that PA²P-15ATA². = Then det(A) =

A: Step 1:   Step 2: Step 3: Step 4:

Q: Find ∣A−1∣ for the matrix

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Q: Suppose that A and B are invertible n x n matrices. Which of the following statements is true. A.…

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Q: diag(a1, ..., an) be a diagonal matrix (i.e., the matrix with the numbers a1, ..., an on the main…

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Q: For each 2 x 2 real matrix A find the canonical form B and an invertible matrix P such that P-1AP =…

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Q: Construct a 3x5 matrix A such that dim Nul 4. Explain and justify your answeT.

A: We need to construct a 3x5 matrix A such that dim Nul A = 4. So, nullity(A) = dim Nul A = 4. We know…

Q: Find all real numbers a, b for which the matrix A nalizable in R. = ( 1] is diago-

A: We have to find all real numbers  for which the matrix  is diagonalizable in

Q: 3. Find m and n so that the matrix below is symmetric:

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Q: Let z be a real number and let A be the matrix 2 I A - (-34). -2 i. Find all values of r such that A…

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Q: 3. Consider the matrices A = |-1 2 2| and B= -1 1 1 -1 -1 (a) Find AT. (b) Compute A². (c) Calculate…

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Q: Use the matrix P to determine if the matrices A and A' are similar. -1 -1 P=[11] 2 p-1 = 6 [2] 15…

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