If A is any invertible n x n matrix, then rref( A) In. %3D True False

Q: MAM™ is similar to A if and only if M is O a. Symmetric matrix O b. Invertible matrix O c Orthogonal…

A:

Q: If a square matrix A is not invertible, then the columns of A could be either linearly independent…

A: We know that if a matrix is invertible then its column are linearly independent. Column A is…

Q: If A is an m xn matrix, then A and AA have the same rank. O True O False

A: Consider the statement  If A is an m×n matrix  then A and ATA have the same rank

Q: If A is an m x n matrix with m <n, then nullity(A) 2 1. O True O False O O

A:

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

A:

Q: If a 6 x3 matrix A has rank 3, find nullity A, rank A, and rank AT. nullity A = rank A= rank AT=

A:

Q: Find values of a for which the following matrix is not invertible: 1 a+ a 2

A: 1a+1a-24

Q: -3 If A is 3 x3 matrix such that A 1 -3 then A is 4 diagonalizable. Select one: True False

A: The matrix of order 3 by 3 will be diagonalizable if it has three linearly independent eigenvectors…

Q: An n x n matrix A is invertible if and only if it is row equivalent to I. 'n' O True O False

A:

Q: If A is an m x n matrix then A' A and A have the same rank. true false

A:

Q: If A can be row reduced to the identity matrix, then A is not invertible. True False

A:

Q: If A is 5x4 matrix, and rank(A) = 1, then its nullity is 3.

A:

Q: Give an example of a nonzero 2 X 2 matrix A such that A2=O

A:

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 A is a nonzero matrix of the form P, then Rank(A) = 2. а

A: Let A be a n×n matrix . If Determinant of A is not ZERO, Then   Rank(A)=n

Q: Find values of a for which the following matrix is not invertible: 1 a + 1 4] 2

A:

Q: (b). Find out the similar matrix of given matrix:

A: Similar Matrices: Ant two matrices A and B are said to be similar if there exists an invertible…

Q: If A is a 5 x 5 matrix then l-A| = |A| |A| O True O False

A:

Q: If A is 3 x 3 matrix such that A 2 then A is -4 diagonalizable. Select one: True False 1 1224

A:

Q: 6. If A is a 4 x 2 matrix and B is a 3 x 2 matrix, what is the size of ABT?

A:

Q: An nxn matrix A is invertible provided the equation A x O has only the trivial solution 0. %3D True…

A:

Q: If A is a skew-symmetric matrix, then for all i, we have a=0. Select one: O True O False

A: Given: A is a skew-symmetric matrix   To find whether the below statement is true or false: For all…

Q: 2. If A is 3 x3 matrix such that A 1 then A is -4 diagonalizable. Select one: True False

A:

Q: For which value of x is the following matrix not invertible: 1 1 2x A = 1 2x 2x 2x 2x 2x 4 1 -1 1 2

A: For a matrix A to not be invertible: dat(A) = 0.

Q: If A is a m × n matrix and B is a n × p matrix then AB is a m × p matrix. True or False

A:

Q: Let A, B, and C be invertible matrices. Then (4A-1B"C²)-1 is equal to c--(B")-1A equal to the above…

A:

Q: A matrix A is similar to matrix B, if for some invertible matrix P, B = P''AP. Prove that if A is…

A:

Q: If A is a matrix such that

A: Given:  A-1=12-1-324 To determine: The value of matrix A.

Q: 4. A matrix A is similar to matrix B, if for some invertible matrix P, B = P'AP. Is B similar to A?

A:

Q: (1) A= BCB, where C is an n x n symmetric positive-definite and B is an n x n symmetric matrix;…

A: In part l, We are given that A=BCB Here, C is n×n symmetric positive-definite. So, xTCx&gt;0 with…

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: 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: If A is n x n matrix, invertible, and B is n × n. Then Col(BA) =Col(B) O True O False

A:

Q: If AB is a 4 x 2 matrix and B is a 1 × 2 matrix, then the size of matrix A is

A: We can multiply two matrices only when the number of column in the first matrix must be equal to…

Q: If A is a 5 x 5 matrix then -A |A| True O False

A:

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: If A is a skew symmetric matrix, what type of matrix is AT ? Justify your answer.

A: If A is a skew symmetric matrix, then our aim is to tell the type of AT matrix?

Q: If an nxn matrix A is invertible, then the rowa of A' are linearly independent. T O True O False

A: If a matrix is invertible then its rows are linearly independent

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…

A:

Q: If A, B, and C are n x n invertible matrices, does the equation C-1(A + X)B¬ = In have a solution,…

A: Given A, B and C are n×n invertible matrices.

Q: Find k for which the matrix below is NOT invertible. 1 1 3 -1 2 1 k

A: For matrix to be non-invertible, it's determinant must be 0. We will use this property to find the…

Q: If A is a constant matrix, the fundamental matrix of the system x' (t) = Ax(t) is non-constant. True…

A:

Q: If A is a 2x2 matrix such that trace(A) = det(A) = 3, then what is the value of trace of (A-!) ?

A:

Q: If A is a matrix and A' is transpose of A, then A' = -A True False

A:

Q: If A is an n x n symmetric matrix and B is any n x n invertible matrix, prove that A is positive…

A: Consider the given conditions. The A = n × n symmetric matrix and B = n × n invertible matrix.…

Q: Find x such that the matrix is singular.

A:

Q: If AB = [0], then A or B is a zero matrix. .. True False

A: We have to find that if AB = [0]  then A or B is a zero matrix is true or false

Q: If A is a skew-symmetric matrix, then for all /, we have a, = 0. Select one: O True False

A: Given: a skew-symmetric matrix A To find: we need to check weather ajj=0, true or false for all j

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.