If you know all 16 cofactors of a 4 by 4 invertible matrix A, how would you find A?

Q: If A is an 7 x 12 matrix, then what is rank A² + dim nul (A²) equal to? Your

A: We can solve this as follows:

Q: 1. Find the cofgctor of 6 in matrix B. 4 り り

A: We will find out the cofactor of 6 for given matrix B.

Q: Suppose that A is a 18 x 7 matrix and the null space of A has dimension 3. What is the rank of A?

A: For a m×n matrix, the number of rows is equal to m and the number of column is equal to n .

Q: Consider an 5 x 5 matrix A satisfying the following two properties: (a) Every row has exactly one…

A:

Q: Let A be an n × n matrix. Is it possible for A2+I = O in the case where n is odd? Answer the same…

A:

Q: If a 6 x 3 matrix A has rank 3, find dim Nul A, dim Row A, and rank AT .

A: We are given that a 6x3 matrix A has rank 3. So, dim(Row A) = 3. We know that dim(A) = dim(Row A) +…

Q: The matrix is not invertible for what value of x 2 1] 3 2 1 1 2

A: The matrix is not invertible the determinant of matrix should be zero.

Q: 32. Construct a nondiagonal 2 x 2 matrix that is diagonalizable but not invertible.

A: .

Q: For which value of x is the following matrix not invertible: 1 1 3x A = 3x 3x 3x 3x 3x O 2 4 O1/3 1

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Q: The 2 ´ 2 identity matrix is:

A: To find:

Q: If A and B are invertible 5x5 matrices, then A+B is also invertible. True False

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Q: If A is an invertible matrix, explain why A and AT must have the same null space. Is this true if A…

A: If A is invertible matrix then it has trivial null space and a matrix is invertible iff AT is…

Q: Is it possible for A3 to be an identity matrix without A beinginvertible? Explain.

A: To explain:It is possible for A3 to be an identity matrix without A being invertible.By definition

Q: Find all the minors and cofactors of the elements in the matrix.

A: Minor of matrix :                                     In a square matrix, each element…

Q: If A and C arę nxn invertible matrices and B is an nxn matrix, then

A: By Theorem we can say that

Q: Suppose A is a symmetric nxn matrix and B is any nxm matrix Show that B'AB, B'B, and BB' are…

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Q: Find a fundamental matrix for the system (3) x′=(1141)x.

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Q: Explain why the columns of an n x n matrix A span R^n when A is invertible

A: From the given information:

Q: Compute the matrix exponential e for the following system x' = Ax. x'1 = 10x, - 14x2, x'2 = 2x, - X2…

A: First we will obtain the metrics A from the given system of differential equation then we will…

Q: Find x such that the matrix is singular. [ х 7 A = -5 2 X =

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Q: which of the following is the cofactor A13 of matrix?

A: Simply omit that raw and column whose co-factor matrix required and write rest all elements in same…

Q: Find diagonal matrix D is similar with A a A =[? -5 And make sure can transtor diagomalizablewith

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Q: Show that A 2 = 0 is possible but AT A = 0 is not possible (unless A = zero matrix.

A:

Q: * Find the Matrix B from order 2 x 4 , Its elements are written in the form by = i + ()

A: Here we find matrix B of order 2×4

Q: 32. Construct a nondiagonal 2 × 2 matrix that is diagonalizable but not invertible.

A:

Q: If A is a 6 × 8 matrix, what is the smallest possible dimension of Nul A?

A: Consider the provided matrix, Given, A is a 6 x 8 matrix. Since, the rank of A equals the number of…

Q: For what values of λ ∈ R is the matrix invertible

A: The matrix A is invertible if and only if its determinant is non-zero.

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: Suppose that A, B, C and D are n × n matrices satisfying the equation ABC = D. Show that if DA is…

A: Given:Suppose that A,B,C and D are n×n matrices ABC=DInvertible matrix:A square matix is invertible…

Q: Assuming that all matrices aren xnand invertible, solve for D. BCA DCB'A = BC?.

A: Properties of invertible matrix:  If a matrix A is invertible and then there must exist a matrix…

Q: Show that the matrix is not diagonalizable.

A:

Q: Show that if a square matrix A satisfies A2 − 4A + I = 0, then A is invertible and A−1 = 4I − A.…

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Q: Construct a 3 × 2 nonzero matrix A such that: Ax = 0 has only the trivial solution.

A:

Q: The matrix is invertible if and only if k#

A: An invertible matrix is a square matrix that has an inverse. A square matrix is invertible if and…

Q: Suppose A is a 10x10 invertible matrix. Then A is row equivalent to the 10x10 identity matrix. A)…

A:

Q: Suppose A is a 5x9 matrix and Rank(A) = 3. Find dim(null(A)). 1 O 2 Оз O 6

A: Solution of the given problem is as follows:

Q: Find x such that the matrix is singular.

A:

Q: ue? 0 0.

A:

Q: 2. Let A be a 7 x 5 matrix, and suppose AB is a 7 x 9 matrix for some matrix B. What must the size…

A: We know that matrix multiplication is possible only when number of column of first matrix is equal…

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: Find a 2 × 1 matrix x with entries not all zero such that

A: Given: Ax=3x, where A=2112 let's assume matrix x is x=ab

Q: If A is a matrix in Rmxn with {()} -5 C(A) = span 2 %3D -2 what is m?

A: If A is a matrix in R^(m×n) then A is a linear transformation form n to m

Q: Suppose A is a 10x10 invertible matrix. Then A is row equivalent to the 10x10 identity matrix. A)…

A:

Q: If a 6 × 3 matrix A has rank 3, find dim Nul A, dim Row A, and rank AT

A:

Q: Find all (a) minors and (b) cofactors of the matrix.

A: Given- 1234 To find- all the minors and co factors of the above matrix. Concept used- For the minor…

Q: Since it is, find the matrix P ^ -1 by using the adjoint matrix of the P matrix.

A: We are given that  We need to find the inverse of p-matrix