A is a matrix and there's a vector x, and Ax is defined. Can the equation Ax=0 have no solution ? Please explain throughly

Q: Let A be 3x5 matrix. Then AX=b has always infinitly many solutions. True False

A: The given statement is

Q: et A be tx8 matrix. Knowing that Nullity (A) = 2. The %3D

A: In the given question, the concept of rank plus nullity theorem is applied. Rank plus Nullity…

Q: if matrix A is ] and matrix B is will have same result matrix. • (AB)T # B'AT 1 Add file if matrix A…

A:

Q: Suppose A is the 3 x 3 zero matrix (with all zero entries). Describe the solution set of the…

A: To prove  Ax = 0

Q: Let A be a 5 × 8 matrix with rank equal to 5 and let b be any vector in R5. Explain why the system…

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Q: Explain why the matrix A + C does not exist.

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Q: Let A be an 8 × 5 matrix of rank 3, and let b be anonzero vector in N(AT ). Show that the system Ax…

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Q: Suppose that Q is an orthogonal matrix, then OaQ-8 ObQ-2 d 1Q-0

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Q: 2 Construct a 3 by 3 nonzero matrix A so that vector is a solution to Ax = 0 -

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Q: e/ By three ways Show that B= %3D isorthogunal matrix

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Q: #16

A: Recall the following facts.

Q: Consider the following matrix and vector: 1 1 A = 1 -4 0 -3 -2 and x = 6

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Q: Let A be 7×9 matrix. Knowing that Rank (A) 3. Then Nullity(A) is equal to: ||

A: Rank nullity theorem Let T:V→W  be a linear transformation on finite dimensional vector spaces over…

Q: Can you please help me th

A: Given,              x1=011, x2=2-10, and x3= 10-2 be eigenvectors of A which corresponds to…

Q: Let A be Sxó matrix. Knowing that Nullity (A) = 2. Then Rank(A) is equal to: * Non

A: Introduction: According to the rank-nullity theorem, Rank(A)+nullity(A)=number of columns in A Where…

Q: 2 Discuss whether the matrix A 1 2 0 is diagonalizable or not. -3 5 2 ||

A: A matrix is said to diagonalizable if for every eigen value's algebraic multiplicity is equal to its…

Q: Construct a 3 x3 nonzero matrix A such that the vector is a solution of Ax = 0. 1 LA =

A: x=-1-1  1 Now let A=abcdefghi be the required vector. Then, Ax=0⇒abcdefghi-1-1  1=000⇒-a-b+c-d-e+f…

Q: Find an example of a singular 2 × 2 matrix satisfying A2 = A.

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Q: The equatiokn  Y = (x,y)T  is given as a vectorfunction with 2 components and A = table below 3 2 2…

A: Given is a matrix A and we have to diagonalize the matrix A. First we find eigenvalue of matrix A…

Q: Show that the matrix; is singular

A:

Q: Show that if a 3×3 matrix A is never sad then the entries along its diagonal, i.e. a11, a22, a33,…

A: Let 3×3 matrix A is never sad

Q: Is there any 2x2 matrix with all non-zero entries, that is not diagonalizable but invertible? If…

A: Solution

Q: Show that the matrix A = singular. 1 -2 3 4 0 5 0 is 60

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Q: When two m x n matrices are said to be equal? Explain there Applicability?

A: Two mxn matrices are said to be equal if their corresponding elements are equal.

Q: Which matrix is not similar to

A: Given that Matrix- X= 011112-12114, A=21-121011114,B=01111411-122, C=0-111-12121-14, D=100030003,…

Q: 2 3 Show that the matrix A is singular. 4 6

A: Concept used: Singular matrix are the matrix that is not invertible. In other words the determinant…

Q: The matrix X1 X = is called a vector.

A: We have to find

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: [2 Given the matrix

A: As per the instructions, we will be solving only the first question. We will be solving 2131xy=21.…

Q: If a square matrix has a row that is a multiple of another row, then it is singular. True or False

A: Answer is true

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: The size of the matrix X'Y, where X is a design matrix of size (k+1) by (k+1) and Y is the vector of…

A: The size of design matrix X is given by (k + 1) by (k + 1)  And Y is the vector of values of…

Q: What is the condition for a diagonal matrix to be orthogonal?

A: use the properties of orhtogonal with respect to a diagonal matrix...

Q: If A is a square matrix whose rows add up to the zero vector, explain why A cannot be invertible.

A: Given A is square matrix whos rows add up to zero vector.

Q: Find a (2x2) singular matrix A that maps (2, 2) into (1, 2).

A: Here in this question find a 2×2 matrix that maps (2,2)  into (1,2). Here i attached solution of…

Q: Let A be 5x6 matrix. Knowing that Nullity (A) = 2. Then Rank(A) is equal to: * None of these O 2 O 1…

A: We will find the rank of A as following.

Q: 2. For what value(s) of h will y be in Span{v1, V2, V3} if 17 57 -3 -4 Vị = -1 V2 = -4 %3D V3 = 1…

A: Given vectors are v1=1-1-2, v2=5-4-7 and v3=-310 Also given y=-43h is in span of v1,v2,v3 So ycan be…

Q: Find a matrix P that diagonalizes 1 0 0

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Q: Either the row vectors or the column vectors of a square matrix are linearly independent. True False

A: Any row vectors or column vectors of a square are said to be linearly independent if…

Q: с pose the vector -6 is in the nullspace of the matrix d 6 -4 34 1 -5 23 1 -7 rmine c and d giving…

A: Topic:- application of algebra

Q: If the first two rows of a matrix A are equal and the matrix product AB is defined, then the first…

A:

Q: Give an example of a matrix A and a vector b such that the solution set of Ax = b is a line in R'…

A: System of linear equations

Q: Suppose A is a 2 × 2 matrix which rotates every vector clockwise by 45degrees . Geometrically, what…

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Q: If you keep the same basis vectors but put them in a different order, the change of basis matrix B…

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Q: Let A be a 5 × 4 matrix. Can the equation Ax=b be consistent for all b in ℝ5 ? Explain, please. Can…

A: Given that, A is a 5×4 matrix. Consider the equation, Ax=b. Here x is a 4×1 matrix with n=4 unknowns…

Q: Show that the matrix is not diagonalizable.

A: Given matrix The characteristic polynomial of is the only Eigen- values are

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.