For each of the following, give an example of a non-zero 4 x 4 matrix A (i.e. non-zero matrix means not all entries are zero) which satisfies the following conditions. I the matrix does not exist, state so and explain why. (a) A is upper triangular as well as lower triangular. (b) A is in row echelon form (REF) but not in reduced row echelon form (RREF). (c) A is symmetric as well as skew-symmetric. (d) A is a scalar matrix and also the identity.

Q: If matrix A is 2 x 5 and the product AB is 2 x 4, then what is the order (or size) of B?

A: is a  matrix is  matrix.We have to find the order of

Q: k 2 2. Consider the augmented matrix Aaug = 0 (1- k) (k2 – 1) k +1 (a) For which value(s) of k is…

A: We get no solution if rank [A:B] is not equal to rank of A.

Q: The diagonal of a square matrix refers to all elements in a line from the top-left to the bottom-…

A: We have to prove that the number of elements in upper diagonal matrix is n(n+1)2. For , n=1 , 4×4 a…

Q: a) Find the matrix of the quadratic form. Assume x is in R3 5x3-x3 +7x3-5x1x2 -3x1x3

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Q: (2x1+3x2 - x3 +3x4 + X5 = 176 | 3x1 + x2-4x3 + 3x4 - x5 = 0 X1 + X2 + 3x3 - 4x4 + 2x5 48 %D X1 + 2x2…

A: The given…

Q: Use the matrix form of the Euclidean algorithm to find the greatest common divisor (165,312) for the…

A:

Q: True or false: The inverse of a full rank 4x4 matrix exists

A: The solution is given as

Q: Perform elementary row operations to transform the matrix [2 3] 5 6 into the identity matrix.

A:

Q: Consider an n x n matrix/grid. Two ants, A and B, are located at opposite corners of the grid (A is…

A: The two ants meet without crossing each other's path if and only if they meet on the main…

Q: Explain why the matrix 80] A B 0 A is not diagonalisable.

A:

Q: If A is a 4 X 2 matrix, explain why the rows of A must be linearly dependent.

A: If A is a 4 x 2 matrix, then it has 4 rows and 2 columns. Each row can be thought of as a vector in…

Q: The matrix A5 x 3 may have a rank = 4 %3D Select one: O True O False

A: Answer:   False  As rank of a matrix is always less than or equal m or n if order of matrix is m x…

Q: (1 b) Write a common matrix with a format (5 x2) form, provide a specific numerical example. Write a…

A: For the solution follow the next step.

Q: Consider the matrix 2 -1 5] -2 We can obtain 1 in the shaded position if we multiply all the numbers…

A: To determine the number by which multiplying in the row shaded position becomes 1.

Q: . How much memory is needed to store a 500 x 500 real matrix using Float64 type? What if the rank of…

A: To calculate the amount of memory needed to store a matrix, you can use the following formula:Memory…

Q: Show that, the non-zero elements of the inverse of a N*N diagonal matrix is just multiplicative…

A: As per the question,we are asked to prove that the non-zero elements of the inverse of a diagonal…

Q: ind the 3x3 matrix that is equivalent in it's action to each of the

A: Given: To find 3×3 matrix that  equivalent to the symmetry operators are, a  S^2zb  C^2z

Q: I'm struggling to understand why there is a 1 at the bottom of the row (first and third example of…

A:

Q: 4. Explain what is wrong with the following "proof" that (ABC)" – C"B" A" for three conformable…

A: Properties of transpose of a matrix: (AB)⊥ = B⊥A⊥ Given: (ABC)⊥.

Q: 2 3-2 10 51 1 2 1 2 1 2 1. Convert the following matrix to row echelon form: LIST ALL ROW OPERATIONS…

A: Row echelon form is a matrix in which all the elements below the pivot element is zero Consider…

Q: "Every 2x2 matrix that can be carried to the 2x2 identity matrix through two reduction is…

A: Every 2x2 matrix that can be carried out to the identity matrix through two reduction is…

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

A:

Q: a) Write the augmented matrix for x + 2y3z = 9 2x - y + z = 0 (4x - 2y + 2z = 0 the row echelon form…

A:

Q: en the definition tr rices (no numbers). (d) = a + d show that tr(A B) = tr(BA) using gen

A:

Q: can you put the answer in matrix form

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Q: s this matrix in row-echelon form or reduced row-echelon form

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Q: B) find the transpose of the matrix A C = 3 2

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Q: Consider the following augmented matrix: 0 0 2 0 3 | -3 5 1 00 1 22 -1 1 a. Is the matrix in…

A: NOTE: Refresh your page if you can't see any equations. . the given augmented matrix is  as we can…

Q: (a) Show that a matrix with two rows and two columns that is in reduced row-echelon form must have…

A: A matrix is in reduced row-echelon form (RREF) if it satisfies the following conditions:Each leading…

Q: If A is n x n matrix, invertible, and B is n × n. Then Col(BA) =Col(B) O True O False

A:

Q: If Y = X(XTX)-¹XT where X is a square matrix and (XTX)¹ exists, then: Statement I: Y is a square…

A: Statement I :Suppose  is a    matrix.Here,                        ( since )               (By…

Q: Provide the symmetric matrix that generates the following quadratic form Q(x): x+2x+3x3 + x₁x2 - 2X1…

A:

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.