what does it mean for two matrices to be similar? If A and B are similar, list all properties that are preserved by them

Q: Due to what property, applied to the matrices below, do we know that A + (−A) = O?

A: A+-A=O

Q: TRUE/FALSE The product of two elementary matrices is an elementary matrix.

A: False.  For example , the matrices are elementary matrices as they are obtained from I2 by single…

Q: Explain the fact “Cofactors are useful when matrices have many zeros”.

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Q: Will AB = BA always be true when A and B are nxn diagonal matrices? Explain why/why not Will AB = BA…

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Q: lues of a 4 x 4 matrix A are given by 2, 1,5, 4, the

A: We have to choose the correct answer from the given option according to the given condition

Q: Which of the matrices that follow are in row echelon form? Which are in reduced row echelon form?

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Q: elementary

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Q: True or false: Matrices of different orders can sometimes be multiplied.________

A: Multiplication of matrices is only possible when the number of columns of first matrix must be equal…

Q: What is a matrix?

A: Definition :                           A rectangular array of m × n numbers ( real or…

Q: What do we mean by the transpose of a matrix?

A: Matrix is a set of number which are arranged in form of rows and columns. They have elements in them…

Q: Explain why two similar matrices have the same rank.

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Q: is it A or B ? if it is A can you write it as an integer or simplified for each matrix element

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Q: Determine whether the statement, 'Two 2 X 2 invertible matrices can have a matrix sum that is not…

A: Statement: "Two 2 X 2 invertible matrices can have a matrix sum that is not invertible" The above…

Q: why is the matrix like that?

A:

Q: Provide an example of an elementary matrix for each of the three types of row operations and clearly…

A: The three types of elementary row operations on a matrix : (1) Interchange two rows (2) Multiply…

Q: Suppose A and B are both 3 × 2 matrices. Which algebraic operations and procedures apply to these…

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Q: Determine whether or not the matrices [5 -3 [5 -1 2 -1 and |4 1 -2 are similar. 3 |2 -1 2 Choose

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Q: Explain this statement "The product AB of two matrices is defined only if the number of columns of A…

A: Let A is a mxn matrix  And N is a pxq matrix. While multiplying two matrices we multiply the rows of…

Q: Find a sequence of elementary matrices whose product is the nonsingular matrix

A: Consider the given nonsingular matrix: Here the objective is to find the elementary matrix whose…

Q: Determine if the statement is true or false. If two matrices are equivalent, then one can be…

A: According to the definition, Two matrices are said to be equivalent if they can be transformed into…

Q: Give an example of two matrices A and B such that BA exists, but AB is undefined. Explain why your…

A: Finding the product of two matrices is only possible when the inner dimensions are the same, meaning…

Q: Explain the fact Every rank one matrix is one column times one row.

A: Every rank of a matrix is one column times one row is not accurately correct.

Q: Find the size of the matrix. Determine if it is 9 6 3 1 39 6 1 9

A: Count the number of rows and columns

Q: A row matrix and a column matrix are also called  ______________ .

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Q: The product of two invertible matrices is always non-zero. Select one: OTrue

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Q: Is the product of two elementary matrices always elementary? Explain.

A: To check product of two elementary matrices will be elementary or not.

Q: Which of the matrices that follow are in row echelon form? Which are in reduced row echelon form?

A:

Q: What do 2 × 2 matrices represent graphically?

A: 2 × 2 matrices represent:

Q: What are the uses of matrices?

A: Matrices are used a lot in the following areas

Q: If possible, express A = 3. as a product of elementary matrices.. 2 3

A: An elementary matrix is a matrix obtained by performing one row operation to the identity matrix.…

Q: The sum of two skew-symmetric matrices is symmetric. Select one: True False

A: Solution in step 2

Q: Which of the matrices that follow are positive definite? Negative definite? Indefinite?

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Q: Let A, B and C be 2x2 matrices that are invertible under matrix multiplication. Simplify (A CBC)as…

A: Since you have asked multiple question, we will solve the first question for you.If you want any…

Q: Two 2 x 2 invertible matrices can have a matrix sum that is not invertible.Determine whether the…

A: ''Two 2 x 2 invertible matrices can have a matrix sum that is not invertible''. We have to determine…

Q: What is the term matrices

A: Matrices :- A matrix is an ordered rectangular array of numbers or functions. The numbers or…

Q: True or false: Two columns of a matrix may be interchanged to form an equivalent matrix.

A: Known fact: Any elementary row transformation of matrix produces an equivalent matrix.

Q: Give an example showing that the rank of the product of two matrices can be less than the rank of…

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Q: We can add two matrices having real numbers A and B if their Elements are same Order is same Rows…

A: This is the basic rule about matrix addition

Q: How can we determine the cofactor for each element in a matrix?

A: Query- How can we determine the cofactor for each element in a matrix? Answer-  The first step…

Q: 3 - 3 1 /- 1

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Q: Find two 2 × 2 matrices such that ∣A∣ + ∣B∣ = ∣A + B∣.

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Q: What are the Symmetric Matrices?

A: we know that if transpose of a matrix is equal to itself, then that matrix is said to be symmetric…

Q: Give an example of a 3× 3 diagonal matrix.

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Q: If A and B square matrices of the same order. then (A+ B)(A - B) is equal to

A: Last option is the correct option. (A+B)(A-B)=A2-B2+BA-AB

Q: True or false: Matrices of different orders can be added._________

A: Two matrices may be added or subtracted only if they have the same orders or dimension that is, they…

Q: Describe when the multiplication of two matrices is not defined.

A: Given, multiplication of two matrices

Q: How did they get the numbers in front of the matrices such as (-1), (-2), (6) and so forth?

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Q: 4. Describe all matrices row equivalent to the matrix: [B]

A: Since you have posted a multiple question according to guildlines I will solve first(Q4)   question…

Q: Find out two examples for each types of matrices and write down it's order also

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.