Give an example of a 3× 3 diagonal matrix.

Q: Diagonalize the matrix A 2 -2 if possible. 2 -3

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Q: Diagonalize the following matrix. A = 6. -1 -1 -2 -1/

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Q: The transpose of a square matrix is

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Q: Explain Row matrix and Column matrix?

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Q: Does the matrix have an inverse? Explain why why not. or

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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: What do you mean by transpose of a matrix? Explain their properties?

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Q: State the dimension of the matrix. [1 4 7]

A: [1 4 7]   From the given matrix , there is only one row that has three elements   In first row , we…

Q: The dimension of the row-space of a matrix equals the number of rows of the matrix. Select one: O…

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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: Matrix A is 2 x 7 and matrix B is 2

A: Given, Matrix A is 2 x 7 and matrix B is 2 x 8.

Q: The product of a 5 ´ 3 matrix and a 3 ´ 5 matrix is

A: When we do matrix multiplication: The number of columns of the 1st matrix must equal the number of…

Q: Illustrate the Skew-symmetric matrix ?

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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: Envision a 2 x 3 matrix.

A: Let A be the matrix with order 2×3, which represents 2 as number of rows and 3 as number of columns.

Q: Explain an example of matrix multiplication.

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Q: What Geometric shapes are obtained from 2x2 matrices?

A: Important points: Geometric shape of all square matrices is 'square'. Order of a general matrix:   n…

Q: Explain the rank of a matrix?

A: The rank of a matrix is defined as the maximum number of linearly independent column vectors in the…

Q: What are the uses of matrices?

A: Matrices are used a lot in the following areas

Q: In an augmented matrix, what does each column represent?

A: Given: In an augmented matrix, what does each column represent?

Q: Give an example of a 2 X 2 matrix that is its own inverse.

A: Given:2×2 matrix

Q: Explain the Main diagonal within a matrix ?

A: The main diagonal within a matrix consists of those elements which lie on the diagonal that runs…

Q: Explain why a matrix that does not have the same number of rows and columns cannot have a…

A: Let A be the matrix of order m × n If inverse exists, then AA-1 =A-1A = I Where I is the identity…

Q: State the dimension of the matrix.

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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: The product of a 2 ´ 3 matrix and a 3 ´ 2 matrix is

A: When we do multiplication: The number of columns of the 1st matrix must equal the number of rows…

Q: Give an example of a 3 × 3 matrix with real inputs that is not similar to a matrix diagonal

A: A matrix is said to be a diagonalisable  if it is similar to a diagonal matrix. Therefore we need to…

Q: Consider the matrix 2 2 A = 1 3 -1 -1 -2

A: Matrix power is obtained by multiplication matrix by itself 'n' times. For  A3 we have to multiply…

Q: Explain the general formula for the inverse of a matrix?

A: Given, Explain the general formula for the inverse of a matrix?

Q: Explain why the matrix is not diagonalizable.

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Q: Diagonalize the matrix, if possible -1 4 -2 A =| -3 4 2 = 1, 2, 3 -3 1 3

A: We have to solve given problem:

Q: Find the adjoint of the matrix.

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Q: . If A= is a symmetric matrix, find the value of x. -x+3 4

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Q: Explain why the matrix is not diagonalizable.

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Q: Find the rank of the matrix -1 3 A = -2 -3 0 1 2 3 -2

A: The rank of a matrix is the number of non-zero rows in the row echelon form of the matrix. We need…

Q: State the Properties of matrix addition.

A: Addition of MatricesTwo matrices may be added only if they have the same dimension. That is, they…

Q: Transpose the matrix -2 -1 2 2 -1

A: The given matrix is:312-2-1002-1To find the transpose.

Q: Diagonalize the matrix -5 -2 A = 3 [ by writing it as A = PDP-1

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Q: Diagonalize the following matrix -1 2 -2 A = 1 -1 -1 0

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Q: Illustrate the Minor of a Matrix element?

A: Minor of a matrix element:

Q: provide an example of matrix multiplication with the solution

A: We have to give example of matrix multiplication.

Q: Perform the matrix operation, or if it is impossible, explain why.

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Q: Identify the size of the matrix. a. A4X7 * B7x12 b. 432x5 + B32x5 c. A3x2 + B3x2 С.

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Q: Find the rank of matrix 1        3 0       -2 5       -1 -2       3

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Q: State the dimension of the matrix.

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Q: Give two examples of a matrix which is its own inverse (that is, where ?^-1 = ?)

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Q: A matrix which is not a square matrix is called a .6 Matrix

A: 6)  A matrix which is not a square matrix is called a

Q: A matrix with the same number of rows and columns is called a __________ matrix.

A: A matrix with the same number of rows and columns is called a square matrix.

Q: matrix is not easy to do with just row operations, because the

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