1 6 3 and C=-2 1 0.Consider the follow 7 0 0] 7 Let A= 5 4 -1 0 list of matrix products: AB, BA, CA. Calculate the matrix products, if poss otherwise explain why it is not defined.

Q: 3. Let A = 1. ). Compute eat in two different ways: (a) by exponentiating the equivalent diagonal…

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Q: 30: If reflection about origin is represented by the matrix R reflect the letter %3D ro 4 4 1 1 01…

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Q: Consider the following matrices: 5 10 0 -1 1 5 103 B and C= O 1 0 2 10 -1 3 1 4 Find matrix A so…

A: NOTE: Refresh your page if you can't see any equations. . . find the inverse of C

Q: Suppose that A (A, then det(B)- Select one: A. 15 OB. 5. OC -15 ODO th ) is a (4 x 4) matrix, where…

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Q: Let A = - 2     1    0                 1     0    1                2    -3    1        A is a…

A: trace is the sum of all diagonal elements of the matrix.

Q: The dimensions of the following matrix is: 2 6 11 4 7 8 1 0 6 7 4 2 [ L6 1 9-

A: dimensions of the matrix261478106742619

Q: 3 1 come up with two matrices D and C such that DA CA but D (b) For A C. 6 2

A: The given matric,

Q: a) Consider the following matrices: [1 0 01 0 0 ,B = |0 0 0,C Lo o 1 1 0 0] 1 2 -1] A =| 2 -1 2 1] 2…

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Q: In cach of the following, write the matrix A as a product SDS, where D is a diagonal matrix. ( ) 10…

A: We have to diagnose the above matrix.

Q: (a) By using the fact that M is an upper triangular matrix, calculate det M, clearly stating any…

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Q: 1 0 0 0 1 0 9. Suppose M Which matrix is M1? %3D 0 3 1 1 00 1 3 0 0 1 0. -3 0. 0. 1 O (1 0 0 0 1 0.…

A: Finding inverse of M

Q: Is the following matrix diagonalizable?

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Q: 4. Verify whether the two given matrices are similar. Justify your an- Swers Question a. 1 A = 1 and…

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Q: Use A-1 =(1/detA)adj A to compute the in­verse of the coefficient matrix 2x -y = 5       x + 3y = -1

A: Given: The linear system of equations is, The inverse of a matrix is calculated by using the…

Q: Consider again 2 × 2 diagonal matrices: k 0 0 j If k, j ∈ {0, 1, 2, 3, ..., 9}, how many possible…

A: Given 2×2 diagonal matrix k00j k, j ∈0, 1, 2, 3, ..., 9

Q: matrix. A= [7   -9      5 0      5      4

A:

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

A: Given that B=QRQ-1 where, Q is orthogonal and R is upper triangular. Then, multiply Q on both sides:…

Q: Compute the indicated matrix by using the following matrices. [ 1 -4 1 -5 0 6 A = 3 C = B = 6. 6 -1…

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Q: 0 0 [1 0 1 0 0 1 01 а. Lo 1] [1 0 1 01 0 1 1 Lo b. 0 0 11 [1 0 0 01 0 1 1 C. 0 0 0 0 0 Lo

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Q: 2 8 Let A = Write 3A. Is det(3A) equal to 3det(A)? 5 6 ЗА- (Type an integer or decimal for each…

A: Given that  The matrix is  To find the det(3A) and 3det(A)

Q: If A is 3 x 3 matrix such that 1 -3 1 1 A 1 -3 Al 1 A 1 1 -3 -2 -4 then A is diagonalizable. Select…

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Q: Let 1 -2 22 -11 1 1 A=0 -1 P= and 0 1 0 %3D -1 100 P diagonalizes A, then compute the matrix A 2577…

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Q: Verify by direct calculation that the matrix -2 -3 -1 A = 1 %3D 3. 3. satisfies the Cayley-Hamilton…

A: by cayley Hamilton theorem , " matrix satisfied its own characteristic equation " now to satisfied…

Q: Match the two matrices A, B with their product AB. i Instructions 1 0 2 6 7 4 3 4 5 -3 9 0 6 1 [1 -2…

A: Match the two matrices A, B with their product AB.

Q: 4. 1 0 13 4 1 -2 15 -1

A: 100010001·2457134-215-17=1·2+0·7+0·-21·4+0·13+0·151·5+0·4+0·-170·2+1·7+0·-20·4+1·13+0·150·5+1·4+0·-1…

Q: Illustrate the Gersgorin theorem by the matrix 2 1+ 2i 0 A = -1 -2 – 2i 1/4 1/41/2 140 12 1/7 1/2…

A: We state the theorem and explain it with the help of the given matrix A.

Q: 1 1 2 1 1 and B = 1 1 2 1 Let A = -1 -4 1 -2 -2 5 -4 1 -6 5 -4 1 2 4 -2 To show A ~ B, it is…

A: Given that A=11211210-1-41-21-25-4B=102012101-65-4204-2 To prove : A~B If two matrix A and B are…

Q: 1. Determine whether the following statement is True or False. Explain why in 1-2 sentences. Let A…

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Q: If A and B are 3×3 invertible matrices, such that det(A)=2, det(B) =-2. Then det (ABA^T) = ???

A: To solve this problem, we use the standard result of matrix

Q: [1 Find a matrix A = -4 -51 = l3. y] 1 z such that A² 10 %3D Lo 1. Lo

A: Given A=1xy01z001 A2-0-4-50010000=I3 To find Matrix A:

Q: 2. Find the LU factorization of the following matrix. 1 1 A = | 1 2 3 1 3 6 /1

A:

Q: Let A be a nonsingular 4×4 matrix with det(A¯1) = - 2 Then det(2adj(A)) 1 8 -2 4 -1 8 None -4

A: Use the properties of the matrix to solve the problem.

Q: Let A = 0 1] 3 03 0 0 2 = If possible, construct P and D such that A don't need to compute P-¹).…

A:

Q: A matrix A and its RREF, R, are shown, below. -2 -14 -1 -5 -6 1 7 0 0 3 | | 0 0 R = 0 0 0 1 35 1 15…

A: The space spanned by rows of A is called row space of a matrix and denoted by row(A) The space…

Q: 3 3 , Let M 1 -2 -3 Find c1, C2, and C3 such that M3 +¢¸M² + c2M + C3I3 = 0, where Iz is the…

A:

Q: Find the matrix A given that -1 2 (I2 + 2A)–1 4 5 O a. 1/13 2/13] -5/13 O b. [-1/13 5/13] 2 -1 4/13]…

A: The given equation is:…

Q: (b) Write the three matrices that are used in Cramer's rule to compute the numerator of the…

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Q: Determine the matrix C such that (CT – 21) 1 1 2 2 3

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Q: Let A be the following matrix 8 8 3 4 5 8 4 2 3 After diagonalization, Pand Dare found such that A =…

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Q: Let A be the following matrix 6 7 4 9 5 9 1 3 4 After diagonalization, P and D are found such that A…

A: We use the following theorem: If A and B are two n by n matrices, then trace of (AB)= trace of (BA)

Q: Use Theorem 1.4.5 to compute the inverse of the following matrix. 12 0 A 3 NOTE: Write the elements…

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Q: 2. Find the LU factorization of the following matrices without pivoting 1 2 3 a) A = 2 5 4 354 1 -1…

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Q: DHI Reduce each Hhe following matriceg Into Me of indicated form. (i):- -2 3-ノ red uced eehelom fom.…

A: Solve the given problem.

Q: Find the matrix product mentally, without the use of a calculator or pencil-and-paper calculations.…

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Q: 1. If A is 3x3 matrix with det(A) = 5 then det(3A) %3D O 3(5)=15 9(5)= 45 O 27(5)= 135 5(5)(5)= 125

A:

Q: 4. (a) Show that the following matrix is diagonalizable. (b) Find a matrix P that diagonalizes A.…

A: A matrix is said to be diagonalizable if the algebraic multiplicity of the eigen value is same as…

Q: 2. Consider the following matrices : 1 2 -1 3 1 and B = 3 2 A = 4 2 -1 -2 5 (a) Find At. (b) Use the…

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Q: -11 -8 -9 -7 -4 6 7 10 Consider the block matrix A = What is A11? -2 -6 11 12 5 -1 1 4 A11

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Q: As = 8 6 4 A," = 1/3 - 1/6 /2 4 2 2 2 4 4 - 1 - ½ 5/6 1/3

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.