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

Q: • The Matrix B from 3 x 2 at by = 1- is 1. 3. 4. 1 -2

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Q: a) If a 7 × 5 Matrix A has rank 2, find dim(Null A), dim (Row A) and rank AT

A: 1) Given  7×5 matrix  rank(A)=2 using rank nullity theorem we have rank A + null A= number of…

Q: For which values of the constants b and c is the follow- ing matrix invertible? 1 b -1 -b

A: The given matrix is 01b-10c-b-c0

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: If A is a 5 x 6 matrix and the sum A + B can be computed, what is the size of B?

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Q: Suppose A is an m x n matrix whose columns are linearly independent. What is the nullity of A?

A: Given A is an m×n matrix whose columns are linearly independent. We have to find the nullity of A.

Q: If A = (aij) is the matrix of the quadratic form 7x + 5x, + 2x – 6x1x2 + 12x1x3 – 10x2x3, then the…

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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: 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: What is a, if A = 2 4 is a singular matrix ? a Simplify (1+x)(1+x²)(1 – x + x?) in descending order…

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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: |a b X y m nl

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Q: Suppose that  |A| + |B| = |A + B| , find a 2x2 matrix for A and B

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Q: 30 is similar-to 0. if and only if The matrix 03 O ant3 O b.a1 Ocaf0 O dat-1

A: We have to solve given matrix:

Q: Let A be an n xn matrix andB=A+1, where / is the identity matrix, then it is possible for A and B to…

A: False

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 an SVD of the indicated matrix.

A: The matrix is given of which SVD is to be calculated so,

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

A:

Q: Find the characteristic equation of the matrix by inspection. 2 -5 9 6 -3 0 0 4 0 0 8

A: Given that: 2-5960-30000400008 The characteristics equation is given by the formulas, detA-λI=0

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: 5. Suppose that A is a 3 x 5 matrix, and the rows of A are linearly independent. What is the…

A: A is a 3x5 matrix. And rows of A are linearly independent. So that dimension of range space of Ax…

Q: Find ∣A−1∣ for the matrix

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Q: Suppose that A+ is a 2 × 2 matrix and that A+ = -A. Show 7.2 that iA is awesome.

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Q: If A is a 4×6 matrix and the dim Nul A​=3,what is dim Col A​? Justify your answer.

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Q: Suppose that A is an 11 x 4 matrix, and that B is the rref of A. If the number of leading columns of…

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Q: If A is an nxn matrix and B is obtained from A by performing the following elementary row operations…

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Q: If A is a 2 x 3 matrix and the sum A + B can be computed, what is the size of B?

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Q: Find the co-factor of element 4 for a given matrix shown below(4 at 2nd row, 3rd column). 1 2 A = 2…

A: Here we have to find cofactor of 4

Q: Suppose CA = I, (the nxn identity matrix). Show that the equation Ax = 0 has only the trivial…

A: Let A be m×n matrix then Rank(A) + Nullity(A) = number of columns of A Where Rank(A) is the…

Q: If A is an m x p matrix and B is a p x n matrix, then their product AB will be?

A: Two matrix can only be miltiplied if number of column of first matrix is equal to number of row of…

Q: Suppose A is a 5x7 matrix and nullity (A)=3, Then the dimension of the row space of A is IS

A: Given, A is 5*7 matrix and nullity(A) = 3 We have to find dimension of row space of A

Q: If AT = A-1, where A is a real matrix, then A is

A: When transpose of A equal inverse of A , then A is

Q: What is the linear combination of the matrices аnd

A: The explanation are as follows

Q: 18. Let A be a 3 x 5 matrix with 2 pivots. What is the dimension of Nul(A)?

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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: O If A is possi ble value of dim Nul AT ? Please explain an 8x 5 matrix, what is

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Q: 3- If A² [45] [95] 091 (1 find A where A is UPF triangula matrix

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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: Suppose that A is a 3×3 matrix and det (A) = -4. What is det (4A)?

A: By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Q: Q1/ Find the matrix below: -5x+2y-4z=5 3x+5y-2z=0 -2y-8z=3

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Q: 6 X1 -1 -5 X2 II

A: Let us consider the system of differential equation X'=AX then the solution of system of equation is…

Q: 3. Consider 3x3 matrix A the 1 A て 1. レ Colculate the adjoint matrix

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Q: Suppose a 6 x 8 matrix A has four pivot columns. What is the dim (Null A)? Is Col A = Rª ? Explain.

A: see below the answer

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

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Q: Find the nullspace of the matrix given as; A=[1 -2 1; 2 -3 5; 1 0 7]

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Q: Show that A is similar to B by showing that A and B are similar to the same diagonal matrix, where…

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Q: Suppose A is a 3 x 4 matrix. If we can successfully multiply A with the matrix B, then which of the…

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Q: Write down what it means for a n x k matrix to be singular.

A: As we know, If matrix is singular then it has determinant equals to '0' For Finding determinant…