D · [. Let M = M" 12 -6 Find a diagonal matrix D and an invertible matrix P such that M = PDP-1. A 12 -6 and P = 1 Now, find formulas for the entries of M", where is a positive integer. Note: D and Pwill not be graded unless you enter something for both of them.

Q: In Excercise 10, find the general form of of the indicated matrices as the span an example 3.17. 10.…

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Q: A B Let m and n be whole numbers. Matrix P is of order/size m x n. Matrix Q is of order/size n x m.…

A: Given that, m and n are whole numbers. Matrix P is of order m×n and  matrix Q is of order n×m. Want:…

Q: Is the matrix A = 1|2 TILL -1 1 1 -1 -1 1 1 -1 1 1 -1 is orthogonal matrix.

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Q: For which values of the constants b and c is the follow- ing matrix invertible? 1 b -1 -b

A: The given matrix is 01b-10c-b-c0

Q: -2 6. What is the diagonal matrix Find an orthogonal matrix Q that diagonalizes A = 6. A?

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Q: 3. Write the list of the seven properties which are equivalent to a matrix being non-singular.

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Q: Find the matrix A if 3 1 4 A = 11 00

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Q: 1 Find a matrix P that satisfies P 1 9 1 2 0 3 0 900 23 1 7 1 1

A: We have to find the matrix P that satisfies the given equation.

Q: REI [1.5 5 -151 2 30 -1 2 1 .5 and C= [-2]. -.5 16. For this problem, let A = a) Use your calculator…

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Q: 6. Find the matrix of the quadratic form. Assume x is in R³. a. 3x} – 2x3 + 5.x + 4x1x2 – 6x1X3 b.…

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Q: 13.) Determine the matrix: s P 6-8 3 ។ -3 the dimension X 10

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Q: -(¹-21) e matrix B x A? and B = (8) What is the entry on the row 2 and column

A: We have to find the 2nd row and 1st column of the matrix BA

Q: 1 31 A = 2 7 . A·B = B · A = I3×3 -2 -4 -5. ]

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Q: Q9. As usual, let In denote the n x n identity matrix. 1 - (a) Find a 2 × 2 matrix such that A² =…

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Q: If A is a 31x24 matrix whose rank equals 10, find dim(Nul(AT)). Your Answer:

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Q: Q1. (b) Determine whether the statement is true or false, and justify your answer. (a) The product…

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Q: Are the dimensions of the bases of a nxn Matrix always n? Can they be n - 1 or n + 1? Is it the same…

A: In the matrices, the dimensions of the bases are related to the vector spaces they represent.  1.…

Q: 16 21 Let A = |-14 -19 Find two different diagonal matrices D and the corresponding matrix S such…

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Q: ind the 3x3 matrix that is equivalent in it's action to each of the

A: Given: To find 3×3 matrix that  equivalent to the symmetry operators are, a  S^2zb  C^2z

Q: Q4: If the matrix A = (; :),s Show that A2- 2A – 21 = 0.

A: We observe that characteristics eqn of A will be x^2-2x-2=0. By Caley hamilton tum put x=A we get,…

Q: +2 17 8 -4.5]

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Q: 6. Prove that I M is an n x n matrix that has a DIOCK Iorm A B (18) where the sizes of A, B, C are k…

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Q: 1 8 Which of the entries in the matrix 2 -3 -7 9 A) 4 B) 1 Ⓒ-3 (D) -6 -61 4 has-37 as its cofactor?…

A: We have to find correct option by finding element whose cofactor is -37

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

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Q: Which of the following is the matrix C that satisfies the equality (CT +312) -1 3 (a) 2 -5 (:) 5 -2…

A: First take inverse on both sides of matrix equation CT+3I2-1=2714. CT+3I2-1=2714CT+3I2-1-1=2714-1…

Q: Q2) Find x for the following matrix 3 1 x| a) -1 3 4= -30 1 ol 1 |1 2 1| b) 12 x 2=0 13 6 xl

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Q: Q5. Suppose B = QRQ-1, where Q is orthogonal, and R is upper triangular. Show that if B is…

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Q: Find R = A + B, given that A has magnitude 4 and is at an angle of 30° above the positive x-axis and…

A: Let a vector be defined as: a=x, y. The magnitude of a is calculated using the formula: r=x2+y2.…