Consider matrix [2 1 3 A = 3 -1 [2 1 1 30] Find the input matrix for the output matrix 20 [10]

Q: For matrix A, B if A – B = O, where O is a null matrix then * A = B B = 0 A = 0

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Q: Find a 2x2 matrix X that satisfies the matrix equation 45 X + 4 6 3 4 X. 1 2 23 x-[] -3 3 X= -1 3 A…

A: Given- 4545x+1023=3412x To Find- 2×2 matrix x such that it satisfies the above condition.

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: Diagonalize the matrix 1 0 -1 A = -2 3 -1 -2 0 2 In other words, you need to find a diagonal matrix…

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Q: Let A be an n × n matrix. Is it possible for A2+I = O in the case where n is odd? Answer the same…

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Q: Consider the following 3 x 3 matrix A and b in R, 1 -4 8 | A = 2 -3 2 1 5 -8 1

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Q: Q2: You have the matrix 2 3 1 4 A = 4 3 5 2 1 4 3 1 How can we get the transpose of matrix A ?

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Q: Q3. Consider the matrix -1 A = -1 1 Compute || A||2 using the SVD of A.

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Q: Is the matrix         1 0 0                               0 1 0                               0 0…

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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: -2 Find the QR-factorization of the matrix A = 1

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Q: 4. Find the standard matrix for T where Ta2) =(2x,+x -2,).

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Q: Suppose that A is an m x n matrix and B is an n x m matrix. Then the equation (AB) = ATBT is always…

A: Multiplication Property of transpose : We know that the transpose of a produce of two matrices will…

Q: -2 1 2 1

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Q: What does it mean to say that A is a matrix with dimension m x n?

A: Our Aim is to tell that what is meant by a matrix A which is havingdimension m×n.

Q: 2 2 3. Transform the given matrix to RREF -2 1 1 -1

A: The given matrix is; 3 2 2 -2 0 1 1 -1 0. Repost the next question.

Q: Find a 3 x 3 matrix A such that 1 -5 A 3 A 1 -3 and -2 A 4 1 -5 A = 3. ||

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Q: Matrix A: 1 3 4 6.

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Q: matrix. A= [7   -9      5 0      5      4

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Q: Find the range of a (2 × 3) matrix B with rank(B) = 2

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Q: for the matrix        4    2  8 A= 4    3  6      3     2   3 What is the element in the third row…

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Q: For the matrix A. det(A) = 16 B. det(A) = -30 C. det(A) = 0 O D. det(A) = 30 OE. det(A) = -16 %3D

A: We try to solve determinant using some elementary row operations.

Q: A matrix A is similar to matrix B, if f invertible matrix P, B = P'AP. Prove is similar to B and B…

A: Given that: A is similar to B such that: B=P-1.AP.

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

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Q: 1 Diagonalize the given matrix if possible: A 4 -1 1 0 4 0 D = and P 0 2 1 3 4 4. D = 1 and P = -4…

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Q: State the dimension of the matrix.   −3 3 7 0   0 1 14 6

A: Given that, the matrix is          -337001146 Here, the number of rows are 2.   &  the number of…

Q: Find the rank of the following matrix: 3 1 0 0 0 0 rank -2 1 1 4 0 4 2 4

A: A=23100000-21140424 Now, R3→R3+R1 A=2310000004240424 C1→12C1 A=1310000004240424 R4→R4-R3…

Q: Find the SVD of the matrix: 1 2 34 A = 0 0 0 0

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Q: 22. If the order of matrix A is m x p. And the order of B is p x n. Then the order of matrix AB is?…

A: The order of Matrix A : m * p The order of Matrix B : p * n To find matrix AB  Multiply both…

Q: Use the method of Example 6 to compute the matrix A10, where 1 0 6 2 A =

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

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Q: Given A = 1 1 0 3 Compute 5A *Matrix

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Q: Compute the indicated power of the matrix.

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Q: Let A be a square matrix and det(A) = 2. If B is the matrix that results when –7 times the - first…

A: Given that: det(A)=2

Q: Use the method of Example 6 to compute the matrix A10, where 1 0 A = -3 2

A: The given matrix is A=10-32. Observe that, A2=10-32 10-32=10-94=10-3·22-122A3=10-94…

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

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Q: Given the matrix 1

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Q: B: find A of the matrix 2 1 3 3 2 -1 -4 3 -1

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Q: A is a matrix of size 2x4, B is a matrix of size 3×2 Cis a matrix of size 2×4 D is a matrix of size…

A: Given: So, BT is a matrix of size 2x3, CT is a matrix of size 4x2, and DT is a matrix of size 3x4.…

Q: If A is invertible matrix, then (2AT) %3D (A) 를 (4-1)" (B) 2 (A-1)" (C) 2 (A")-1 (D) 글A-1 (E) AT

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Q: Find the rank of the following matrix. -1 3D1 0. 3. 4 2 1 4 |

A: given matrix is -1-100002340-213-104find the rank of the matrix

Q: Find the minor M12 and cofactor A12 of matrix A. 1 6 A = 3 3 -2 0 1 8.

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Q: Give the rank and the nullity of the matrix. 20 -2 A = rank(A) = nullity(A) =

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Q: 1- the rank of the matrix A.

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Q: Consider matrix [2 1 A = 3 2 l2 1 -1 1. [30] Find the input matrix for the output matrix 20 lio]

A: Given matrix  A=21332-1211

Q: Suppose that A is an n × n matrix satisfying the equation A4 + 2A2 − 3A − I = O , where I is the…

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Q: If A is an n × n matrix, what are the entries on the main diagonal of A − AT ? Justify your answer.

A: Given A is an n x n matrix, we need to find the entries on the main diagonal of A- AT. Consider a 2…

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

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Q: Consider an n x p matrix A and a p x m matrix B. If ker(A)-im(B), what can you say about the produet…

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Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.