30 24 Let A = - -32 -26 Find a matrix P, a diagonal matrix D and P-¹ such that A = PDP-¹. P= E D = P-¹ 188 = 10

Q: Find the 2, 3-cofactor of the matrix 1 2 0 0 2 1 -1 7 -3 0 0 0 7 1 0

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Q: Demonstrate that A A-1 = A-1 A = I

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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: /1 3 21 2 1 1 A = 4 03/ -(² 7 1 -1 -1 Find the matrix A. 1 3 03 -3 7

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Q: Find 2 × 2 matrices A and B such that т 6 ]A+[, -1 JA+I 5 -5 ]B = [ 4 -6. ] and -2 -1 4 0 -2 -4 3 -4…

A: Given: The equations  06-1-1A+5-534B=4-60-2T0-211A+-4-8-3-6B=3-47-3T

Q: 8. (3pts) Let A and B be arbitrary n x n matrices. Multiply (A – B)(A+ B).

A: As we know that (A-B)(A+B) = AA+AB-BA-BB=A2+AB-BA-B2here AB need not to be equal to the BA. Because…

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…

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

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Q: Use the matrix P to determine if the matrices A and A' are similar. -1 -1 - 13 6 6 6 P=[¯1 ¯2]·…

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Q: Let I be the rdentity of nxn. Please Compute 3. matrix the matrix funct ions CosT I (i²=-1)

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Q: Find matrix X:   3.     6     5     4     -2   *X=     18     49     -20     6

A: The detailed solution is given below Thank you

Q: -5 4] -5 2 1 ||

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Q: For Square Matrix A, B of the same size is it true (A + B)-1 = A-1 + B-l? Explain

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Q: Find the trace of the matrix 3 A 2 -2 tr(A)

A: The given matrix is A=-332-2. Find the trace of the matrix A as follows.

Q: Determine all the n × n− matrix A with the range such that A2 = A.

A: Clearly the zero matrix and identity matrix are the trivial examples of our problems. However there…

Q: Let matrices A,B,C store factory value of 3 items for the last 20 years, and D,E,F store sale value…

A: Given that, matrices A,B,C store factory value of 3 items for the last 20 years and D,E,F store sale…

Q: What is the linear combination of the matrices аnd

A: The explanation are as follows

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.…

Q: Find a non-zero 2 x 2 matrix such that -5-2 6 15 -[88]- =

A: We have to find a non zero matrix such that the given rfelation satisfies.

Q: Prove or disprove: If the columns of a square n ×n matrix M are linearly independent, so are the…

A: Linearly independent and dependent vectors

Q: Find the LDU factorization of -2 -2 6 4 -15 -10 A = -6 3 -13 -14 -2 14 46 35 That is, write A = LDU…

A: Given A=−2−26425−15−10−63−13−14−2−144635. Find the LDU factorization of A.

Q: Let I be the 2 x 2 identity matrix. What is det (-41)?

A: The given data is:  I be the 2×2 identity matrix  To find det-4I Given:  I be the 2×2 I=1001

Q: N.N て1 て てー -3 こ 1. そー ) Find oenk of the matrix p

A: See the attachment

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…

A:

Q: Let A be 3x3 matrix where det(-A) = 2 2007 let B =030 Then det(A BAB) = L004 Answer:

A: Properties of determinant: det(-A)=-det(A)det(A-1)=1det(A)det(AB)=det(A)·det(B)det(An)=(det(A))n If…