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

Q: If a 3 × 8 matrix A has rank 3, find dim Nul A, dim Row A, and rank AT.

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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: 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 (A, then det(B)- Select one: A. 15 OB. 5. OC -15 ODO th ) is a (4 x 4) matrix, where…

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

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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: If matrix A is 12 xc and matrix K is 4 x t, their product AK is r x 7, what are the values of c, t,…

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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: The matrix is not invertible for what value of x 2 1 1 1 31

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Q: Suppose that Q is an orthogonal matrix, then O a lQ°| = 4 O b. Q°| = 2 O d. Q°| = 0

A: This question is related to Linear Algebra

Q: 2. А %3D [0.7 0.1 Lo.1 0.7

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Q: If A is 3 x 5 matrix with rank 1, then the number of special solutions to Ax = 0 is %3D O is

A: Since the rank of the matrix = 1. So the number of free variables = 5 - 1 = 4.

Q: Suppose A is a 8x4 matrix such that rank(A) = 3. Find dim(col(A)-). dim(col(A)+) =

A: To find: dimcol(A)⊥ Given information: A is 8×4 matrix such that rank(A)=3. Concept used:…

Q: Let A and B be 6 × 5 matrices. If dimN(A) = 2, what is the rank of A? If the rank of B is 4, what is…

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Q: 2. Suppose that A is a 3 x 3 matrix that satisfies A = A 12 (a) Show that the rank of A is at most…

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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: Suppose A is a 5 x 5 matrix for which det(A) = -3. What is the value of det(2A)? det(2A) =

A: Sol:- Given :- Det(A) = -3 and Dimension of 5 * 5 Matrix

Q: If the order of the matrix A is (3x 5) and Bis (5 x 6) then the order of the matrix (A B) will be O…

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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: Suppose that A is a 4 x 4 matrix with det(A) = 5. Then + (24–1) - [2 Enter your answer exactly, as a…

A: We have to find determinant

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: 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: FInd the Solution by Considering Attachment.

A: The method of mathematical induction can be followed to prove above result. Now, The given matrix is…

Q: Consider the matrix below A= 3 -2 4 0 -6 7 a 1 2 -2 1 -3 -4 3 1 2 Find the minor and cofactor of a

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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: 2 - matrix A and that h(T) = T? – 2T – 7 -

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Q: Let Q be an m xn matrix with n >n and orthonormal columns, then we have both QTQ = I, and QQT = Im…

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Q: IF a 4*5 Matrix A has rank 2 , find dim(Null A), dim (Row A) and Rank A^T

A: Using Rank Nullity Thereom,

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 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: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists)

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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: An identity matrix is represented by... О а. Нн-1 O b. H-1H О с. Нн-1н

A: If we multiply a matrix by its inverse we get the identity matrix.

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

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Q: 1. Suppose (B – C) D = 0, where B and C are m x n matrix and D is invertible. Show B = C

A: ( B - C )D = 0 where B and C are m × n matrix and D is invertible.  Then, we have to prove that B =…

Q: 13. Suppose that a 3 × 3 matrix A factors into a product 1 0 1 Determine the value of det(A).

A: It is known that for n×n matrices A and B detAB=detAdetB                      (i) Given…

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

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

A: Given; A is a 5*9 matrix and Rank(A)=3.

Q: If G = | is alx1 matrix, and A is a 1xn matrix, is it true that XA = GA for %3D any number A. Is it…

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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: Consider the two matrices: 2 4 1 B= -5 A= -3 Compute A+ 3B. The result is equal to:

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Q: -0 의 B=[ 1 c=, 이1 1-0 1.where j--T, expres (a) Q3/B: If A = A.B, (b) B. C, (c) C.A and (d) A² in…

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Q: • The Matrix B from 3 x 2 at b, = -1+; is го 1. 2.

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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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