Suppose A is an x n matrix. (a) If ker(A) = (b) Give an example of a matrix with ker(A) = im(A). im(A), what is A²? Explain.

Q: Find an SVD of the matrix. -6 5 A = 0 6

A: We have to general eigenvalue and eigenvectors to find Singular Value Decomposition of matrix A We…

Q: Give an example of a 4 x 4 matrix that is symmetric, has with the (2,4)-entry equal to -5, and has…

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Q: An mxn upper triangular matrix is one whose entries below the main diagonal are zeros, as is shown…

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Q: 6. Find the inverse of the matrix if it exists by using elementary row operation, 2 4 1 -1 1 -1

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Q: Find the characteristic equation of the matrix by inspection. 4 2] -6 0 0 6 0 0 5] 4 -9 LO

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Q: Diagonalize the matrix 1 0 -1 A = -2 3 -1 -2 0 2 In other words, you need to find a diagonal matrix…

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

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Q: why is the matrix like that?

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Q: Due to what property, applied to the matrices below, do we know that A + B = B + A?

A: Due to Commutative Property Of Addition of matrices, we can say that: A+B=B+A. Where, A,B,C are…

Q: Find the inverse of the matrix using Gauss Jordan method?

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Q: |a b X y m nl

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Q: What is the name of the matrix, Sij?

A: Sij is called as similarity matrix.

Q: Some ecologists divided a female bird population into three categories: juvenile (up to 1 yr old),…

A: Here we have to use matrix multiplication to find number of birds of each category

Q: What is the rank of the matrix?

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Q: find an LU factorization of the given matrix.

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Q: Disprove that the rank of a matrix is equal to the number of nonzero rows.

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Q: Suppose A is a 5 x 5 nonsingular matrix, and Bis the result of exchanging the second and fourth rows…

A: If a matrix A is non-singular then all the rows and all the columns  of A are linearly independent.

Q: Find the characteristics equation of the matrix [1 2 A -2 -1 01 and hence find A-.

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Q: If A is a 31x24 matrix whose rank equals 10, find dim(Nul(AT)). Your Answer:

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Q: Find the range of a (2 × 3) matrix B with rank(B) = 2

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Q: Find a matrix B in reduced row echelon form that is rowequivalent to A, using elementary matrices.

A: Given- 2-40013006 To find- Find a matrix B in reduced row echelon form that is row equivalent to A,…

Q: 6. If A is a 4 x 2 matrix and B is a 3 x 2 matrix, what is the size of ABT?

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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: Let A be a 4 × 4 real symmetric matrix witheigenvaluesλ1 = 1, λ2 = λ3 = λ4 = 0 What type of matrix…

A: Given, A is a 4×4 real symmetric matrix with eigenvalues 1, 0, 0, 0. Now we have to find what is the…

Q: Consider the multiplication AB is existing with the size (M × N) , where B is a matrix of size (L ×…

A: Consider the given information. The multiplication of two matrix is possible if and only if the…

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

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Q: What is trace of matrix (2A+3B)

A: Find the trace of the matrix(2A+3B)

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

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Q: Let A be a 3 x 10 matrix, and let B be m x n. Suppose that B'A' is a 21 x 3 matrix. What is the…

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Q: Explain the rank of a n*n non-singular matrix?

A: Consider Use the property of rank which states

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: (4) Let A be a 3x3 matrix. If |4|= 2 , then |3.4|=,

A: Given that A be a 3*3 matrix and |A|=2. To find the value of |3A|

Q: 4. A matrix A is similar to matrix B, if for some invertible matrix P, B = P'AP. Is B similar to A?

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Q: Which one of the following matrix is a Lower triangular matrix?

A: A triangular matrix is a special kind of square matrix in linear algebra.    Find: Which one of the…

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.

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Q: Let matrix A be 2 by 2 matrix and 1 A. 4 and 1 4 .2) 2 Then what is A=? ||

A: At first we will suppose a matrix A as 2x2 matrix and simplfy second condition by pre multiply by A…

Q: To divide the LHS by a matrix on the RHS, what steps do you follow?

A: To find: To divide the LHS by a matrix on the RHS, what steps do you follow?

Q: 4 Is the matrix a linear combination of the ma- 3 and 1 ? Justify your answer. trices

A: A matrix A can be expresses as a linear combination of two matrices B and C, if and only if there…

Q: If A is 3 x 2 matrix and B is 2 x 3 matrix, then AB is always: a. Invertible matrix b. singular…

A: We know that rank ofAB is always less then or equal to min{rank(A), rank(B) }

Q: hat is the matrix for

A: Given, consider the two-tank system shown below. Each of the two tanks contains 200 gallons of water…

Q: Find a family of the matrices that is similar to the matrix -2] 寸 -3 4-

A: Since, you have posted multiple questions but according to guidelines we will solve first question…

Q: what is the Dim of a matrix, like if there is Matrix A, what is Dim(A)? Can i have example too?

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Q: 1- the rank of the matrix A.

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Q: What is a column matrix?

A: Definition of column matrix – A vector which is represented with a list of number is called a column…

Q: Suppose A is a matrix of order p × q and B is a matrix of order q × r, then illustrate the order of…

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Q: Some ecologists divided a female bird population into three categories: juvenile (up to 1 yr old),…

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

A: Given that: A=-3528-13