20. The following are rules of transposition of a matrix except: (explain) a. (A")" = A b. (A + B)" = (A)" + (B)" c. (cA)" = (c)" (A)" d. (AB)" = (A)"(B)"

Q: Find the characteristic equation of the matrix: 4 C = 2 -2 2.

A: Characteristic equation of the matrix C is given by  det ( C - λI ) = 0

Q: Solve the following problems by using the inverse of the matrix involved. (a) An automobile factory…

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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: 17- Let A be 5 x 5 matrix and det(4) = 2. What is the value of der(24)? a) 128 b) 32 16 64 LEave…

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Q: 1 2 0 1 2 3

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Q: Q2: You have the matrix 2 3 1 4 A = 4 3 5 2 1 4 3 1 How can we get the transpose of matrix A ?

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Q: How is the matrix of R^−1 obtained from that of R in general, that is, when A = {a1, . . . , am}, B…

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Q: Is the matrix         1 0 0                               0 1 0                               0 0…

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Q: Demonstrate that A A-1 = A-1 A = I

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Q: A is 5x6 matrix, the range of transformation x->Ax may be IR5 Is this true or false?

A: The given statement is false.Counter example:

Q: 3. Let A [1.1 -0.1] [0.3 0.7 0.7] Is matrix A invertible? How do you know?

A: An invertible matric is a matrix  for which matrix inversion operation exists . A matrix is said to…

Q: 3 Is the matrix a linear combination of the matri- and o o1? Justify your answer. ces

A: A matrix A is said to be expresses as a linear combination of two matrices B and C, if and only if…

Q: 5 -1 5 1 6. -1 6 2

A:

Q: 0 4 13 4 0 -7 0 0 1

A: line of reflecton of a matrix is same

Q: 2 Discuss whether the matrix A 1 2 0 is diagonalizable or not. -3 5 2 ||

A: A matrix is said to diagonalizable if for every eigen value's algebraic multiplicity is equal to its…

Q: 2 -3 For matrix A = -2A? will be %3D -1 4

A: See the attachment.

Q: (18) Does a 2 × 2 diagonal matrix commute with every other 2 × 2 matrix?

A: We have to check

Q: What do you mean by Matrix trace?

A:

Q: In plain-speak, what is a matrix?

A: Definition of matrix helps to get the answer to the problem. There is a wide application of matrix…

Q: 2 4 8 Suppose that A = LDU = 039 , then the matrix U is 0 0 7 equal to: 2 00 0 3 0 0 0 7 1 2 4 0 1 3…

A: Given:Suppose A=LDU=248039007To find : Matrix U

Q: Consider matrix A. -3 5 2 A = 8 -1 3 What matrix results from -8·A?

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Q: [30 If A= 2 0 LO 1 2 −2], find adjoin matrix 1

A:

Q: 22. If the order of matrix A is m x p. And the order of B is p x n. Then the order of matrix AB is?…

A: The order of Matrix A : m * p The order of Matrix B : p * n To find matrix AB  Multiply both…

Q: Diaganolize the following matrix. 0 0 -1 -1 0 0 3

A:

Q: 2.4. Explain why: (a) If the third column of B is zero, then for any matrix A, the third column of…

A: Matrix: A matrix is a rectangular array represented in the form of or Here A represents the matrix…

Q: 6. () Is the following statement True or False? When a coefficient matrix is in reduced echelon…

A: Given statement is : When a co-efficient matrix is in reduced echelon form, the only members in the…

Q: 16- Find k for which the matrix below be Involutary matrix. 4 4 3 3 b) 3. -2, Leave blank *0 ఇ

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Q: Suppose A is invertible and you exchange its first two rows to reach B. Is the new matrix B…

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Q: 3 2 2 3 1, find the matrix B Such that AB = 5 3 4 3 4 2 1 6 1 5 6 4 , If A = 1

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Q: If B arises from a matrix A by elementary row operations, what is the relationship between NS(A) and…

A: Given matrix B arises from a matrix A by elementary row operation. We have to find the relationship…

Q: Describe in your own words the meaning with respect to a matrix of the notation shown below .

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Q: (1) Without calculations, can you tell if the n x n matrix 1 2 ... 1 n – 1 ... 0 0 1 ... is…

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Q: 2) Find the rank of the matrix A = 2 3 -1 ー1 1- ー2 -4 3. 3 -2 3. By deducing imto Echelon form.

A:

Q: 1. Suppose that we have a n × 10 matrix (n rows and 10 columns) where the entries are either 0 or 2.…

A: Just think for different values of n and you will notice that n=2 will work

Q: 20. The following are rules of transposition of a matrix except: (explain) a. (A")" = A b. (A + B)"…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 6. Give an example of two matrices, A and B, neither of which contains any zero entries whose…

A: Below mentioned a example related to this, you can construct many.

Q: 3. Choose the matrix that is equal to the matrix below. 0.82 2 12 4 5 9 19 082 2 0.6 [B] 12 4 10 3…

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Q: (9) If 2 0 0 1 3 A-'B-1 and A = 2 -1 evaluate the matrix B.

A:

Q: What is the matrix X if  3 1 -1 2 X= 3 4 1 2

A: In the given equation, the matrices can be represented by A and B and written as,

Q: Is the answer in #1 and #3 not in matrix form? how so?

A: Remember : eB represents coordinate matrix of e with respect to basis B. Which means if we consider…

Q: 1- the rank of the matrix A.

A:

Q: 1 Find the condition number of matrix -2 -3 4

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Q: 3. Suppose A is an m x n matrix whose rows are all identical and B is an n x p matrix whose columns…

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Q: 1 What is the transpose of matrix -2 0 2 3 -1 3 3 -2 0 a. 0. 2 3 -1 b. 10 -1 -2 2 3 3 C. 1 0-1 -2 2…

A:

Q: Let A be a 5 × 4 matrix. Can the equation Ax=b be consistent for all b in ℝ5 ? Explain, please. Can…

A: Given that, A is a 5×4 matrix. Consider the equation, Ax=b. Here x is a 4×1 matrix with n=4 unknowns…

Q: you have the matrix 30 1 A = |-1 2 0 3 1 2 Very specific inverted?

A:

Q: State True or False: If for a square matrix A and B, null matrix O, AB =O implies BA=O: * False True

A: Given that A and B are square matrices O is a null matrix. Is it true if AB=O implies BA=O

Q: In statistical theory, a common requirement is that a matrix be of full rank. That is, the rank…

A:

Q: Consider matrix A. -3 52 A= 8. -1 3 What matrix results from -8-A?

A: Given that: A=-3528-13

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.