If A has dimensions m×n and B has dimensions n×r, then AB has dimensions, is this true or false and why?

Q: &Suppose that a linear system has its augmented matrix as follows: [3 2 1 1 0 1 3 2 0 1ca] For which…

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Q: Suppose the trace of a matrix is equal to 10. If this matrix is also an identity matrix, how many…

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Q: If the matrix A is of order 2x4, then the rank of A is: Select one: O a. Greater than 4. O b. Less…

A: 1. If the matrix is of order 2×4, then the rank of A2. consider the vector space V with dimension=n,…

Q: In order to determine the unique solution of a linear system Ax b (b0), where A is a non-singular…

A: This question is belonging to the system of the equation in which we have to find the correct option…

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

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Q: If you multiply a 2x3 and 2x3 matrix the size of the resulting matric is A. 3x2 B . 3x1 C. 2x3…

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

A: By Theorem we can say that

Q: The nullspace of a 5 by 5 matrix contains only x = 0 when the matrix has ___ pivots. The column…

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Q: Suppose that the augmented matrix of a system of linear equations for unknowns x, y, and z is 1 0 4…

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Q: If A is a 4 x 3 matrix and b = a, + 3az , then the system Ax = b is consistent Select one: True…

A: If the system Ax = b is consistent, Then b can be written as Linear combination of column vectors of…

Q: If a 3 x 4 matrix has 3 pivot columns, then its columns span R. True False

A: A 3×4 matrix have 3 rows and 4 columns, in each column has 3 elements. Given that matrix have 3…

Q: Suppose a 4x8 coefficient matrix for a system has four pivot columns. Is the system consistent? Why…

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Q: 2. Suppose we have a 6 x 6 matrix A. a. If the homogeneous system Ax = 0 has infinitely many…

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Q: If a 4x5 matrix A has rank 4, find nullity A, rank A, and rank A". nulity A-[ rank A- rank AT-O

A: We have to solve given problem:

Q: Suppose a 3x6 coefficient matrix for a system has three pivot columns. Is the system consistent? Why…

A: Given, 3×6 coefficient matrix. Three pivot columns.

Q: Suppose A is an n x n invertible unit lower triangular matrix and n > 10. A programmer claims that…

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Q: Suppose the only solution of AX-B is the zero matrix (A is nxn and B is nx1). Then the RREF of A| B…

A: We can solve this using given information

Q: Could a rref matrix look like | 1 0 0 1 | | 0 1 0 1…

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Q: Suppose A is ann x n invertible unit lower triangular matrix and n » 10. A programmer claims that as…

A: We will use the basic knowledge of LU decomposition to answer this question.

Q: If A is a square matrix, then a pivot in every row means that the equation Ax=b has infinite…

A: Solution : Given statement is False

Q: following system: x+4y+6z=13

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Q: So is there more than one correct outcome to a matrix in row ecehlon form? If each row has leading…

A: To determine: If there is more than one correct outcome to a matrix in row echelon form. If each row…

Q: If the rank of a 7x9 matrix A is 7, what is the dimension of the solution space Ax =0? The dimension…

A: The dimension of the solution space is 9 - 7 = 2.

Q: Suppose A is an n x n invertible unit lower triangular matrix and n » 10. A programmer claims that…

A: We will use the basic knowledge of LU decomposition to answer this question.

Q: If the rank of a 5x9 matrix A is 2, what is the dimension of the solution space Ax= 0? The dimension…

A: If a be an m×n matrix and r be the rank of a. the solution space of the system of AX=0 is a subspace…

Q: If A is a 4 x3 matrix and b a, + 3az , then the system Ax = b is consistent Select one: True False

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Q: Suppose that A is an 2x3 matrix and B is an 3x1 matrix. Then AB is 2x3 matrix True False 00

A: To find- Suppose that A is an 2×3 matrix and B is an 3×1 matrix. Then AB is 2×3 matrix True False

Q: Suppose M is a (6x6) matrix such that the dimension of its column space is 5 .Then the rank of M is…

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Q: If a matrix A is nonsingular then the number of solutions to the linear system Ax = b depends on the…

A: Here, in the system Ax=b, A is the non-singular matrix. That is determinant of A is non-zero.

Q: If the null space of a 7 × 6 matrix  is 5-dimensional, what is the dimension of the column space of…

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Q: If a 4x7 matrix A has rank 2, find nullity A, rank A, and rank A. nullity A =| rank A = rank AT

A: The given question has been solved in step 2.

Q: and B are square matrices with dimension 2 x 2, C is a matrix with 5 columns. What should be the…

A: Matrix CD is square matrix because A is square matrix.  And CD is define if column in C is equal to…

Q: Suppose M is a (3x3) matrix such that the dimension of its column space is 2.Then the rank of M is…

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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: 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: Let A be a nonzero 3 x 6 matrix. (a) What is the maximum rank that A can have? (b) If rank(A|B) = 2,…

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Q: If A is m x n matrix and Ax b has no %3D solution for some b. then

A: The rank r of a matrix is the number of column (row) pivots, it must be less than equal to m and n.…

Q: Suppose that 4x7 matrix has 4 lead terms. Then collA) = IRt and NIA) = R³ True O False

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Q: If the equation Ax = 0 has only the trivial.solution, then A is row equivalent to the nxn identity…

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Q: If the matrix AB is invertible, must it be the case that BA is invertible? (Note: A and B need not…

A: Here, suppose A=10 & B=10

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

A: Let A be 3×5 matrix . The matrix equation is: AX = b; where A is the coefficient matrix, X is the…

Q: Let A be a 3 x 3 matrix with two pivot positions. Does the equation Ax = have at least one solution…

A: Given A is a 3×3 matrix with two pivot positions. To find if the equation Ax=b has at least one…

Q: 3. Suppose A is an m x n matrix whose rows are all identical and B is an n x p matrix whose columns…

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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: Suppose that we have a n × 10 matrix (n rows and 10 columns) where the entries are either 0 or 2.…

A: Given that the order of matrix is n×10 in which the entries are either 0 or 2. If n=10 and choose…

Q: In statistical theory, a common requirement is that a matrix be of full rank. That is, the rank…

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Q: If the rank of a 4x7 matrix A is 2, what is the dimension of the solution space Ax = 0? The…

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.