consider the following definitions: 1. a submatrix of an matrix A is any smaller matrix obtained by removing one or more rows and / or columns of A 2. the rank of a matrix Amxn can be defined as the largest integer p for which some of submatrix p x p of A has non-zero determinant. If A is square, with det(A) ≠ 0, the opposite of A is the number of lines (or columns). Using just this definition of rank and properties of the determinants to simplify the calculations without scaling the matrix determine all possible values ​​of the parameter t, for matrix A, then have rank 2. Show mathematical argument and justify your answer

Q: Suppose that A is a 18 x 7 matrix and the null space of A has dimension 3. What is the rank of A?

A: For a m×n matrix, the number of rows is equal to m and the number of column is equal to n .

Q: Consider the following system of equations: (image) It is given that the determinant of the…

A:

Q: What is the determinant of a matrix that has been row reduced? For example, calculate the…

A: Let the given matrix is                      A=a11a12a13⋯a1n0a22a23⋯a2n00a33⋯a3n⋮⋮⋮⋱⋮000⋯ann The…

Q: A and B are n x n matrices. Check the true statements below: OA. If det A is zero, then two rows or…

A: Let A and B be matrices of size n x n . Here we need to pick a correct or true statements   Then the…

Q: A = 060 4 1 2 20 04

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Q: Consider the following matrices: 0.2 0.5 -0.2 1.0 -0.5 10 -2.0 2.0 -1.0 Perform each operation in a…

A: Aa per our guidelines, we can answer only first three sub-parts. Kindly repost the rest sub-parts…

Q: 4. Determine whether the given matrix is invertible without computing its determinant. -3 0 1 3 5 8…

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Q: Show that the matrix X -1 : -1 -1 X : 0 : : X is Positive Definite if x > √n −1 The lower right…

A: The given matrix is An=x-1...-1-1x00::⋱:-100x. To Prove: This matrix is positive definite if…

Q: Įsin x cos^(3/2) x dx * O -2/5 cos^(5/2) x + C O None of the choices -5/2 cos^(5/2) x + C O -2…

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Q: The determinate of Matrix A is: * 3-2 A = [1 4 0.5] 2 3 O 16.5 O 1.5 O 11 Non

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Q: Let A, B and C be three n x n invertible matrices with A² = A. Solve the following matrix equation…

A: Given ,  are three  invertible matrices with    .And    Since  are invertible matrices, exist  .

Q: 8. Let A be a square matrix of order n > 3, and suppose that det(A) = 3. Find the following…

A: Given: A is any matrix with detA=3. To Find: det(A3), where A3 is the matrix obtained by rearranging…

Q: 1.) Find the determinant of the matrix A 4200 71 01 1006 0301

A: The given problem is to find the determinant of the given matrix A of 4*4.

Q: Select all statements from below options that are true for ALL invertible n x n matrices A and B DA.…

A: To find correct option from given question.

Q: Which of the following is FALSE? A. Det (AB) = Det (A) + Det (B) B. Det (AB) = Det (A) Det (B) T C.…

A: The False statement is  Det(AB)= Det(A) + Det(B)

Q: 5. Let D be a non-singular matrix such that 7. (7D)- 1 -2 Find D.

A: Inverse matrices

Q: Show that every 2 x 2 matrix A of determinant 1 is the product of three elementary matrices. This…

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Q: Let A be a 4 × 4 matrix with det(A) = 2. Which of the matrices 2A, -2A and A² will have a…

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Q: Create a 5 x 3 matrix, call it A, with no more than 3 zeros such that the columns of A are linearly…

A: Let us consider a matrix A=-4-300-14103546-7-3-9 First we will show that columns of matrix are…

Q: If A is square matrix, the determinates of its element will be: [1 6 21 A = 4 1 6 4 o] l1 .a det(A)…

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Q: Exercise 7.4.1 Use row operations to calculate the following determinants: 12 1 2 (a) 1 2 1 23 2 -4…

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Q: 5. Prove that if A is a non-singular matrix that multiplying one row by an non-zero constant and…

A: We need to prove given statement.

Q: Which of the following statements is/are correct? Please select one or more: For every matrix A,…

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Q: Let A be an n x n matrix. Are the following statements true or false? ? 1. If 5 = 0 then det(A) = 0.…

A: Approach to solving the question: refer the answer above Detailed explanation: Examples: Key…

Q: Let A be a (12x12) matrix such that the dimension of its column space is 12. Then Select all…

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Q: If P is an invertible n × n matrix, show that: det(P−1A2P) = (det A)2 using the determinant…

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Q: Suppose that A and B are n x n matrices, where B is nonsingular. Prove that the determinant of BAB-¹…

A: We use properties of determinant.

Q: If ri is a first row of a square matrix A and r3 is the third row of A such that ri = 2(r3) then |A|…

A: By applying elementry row operation we can find the value of |A|

Q: Let A E Rx and B E Rmxm and assume that dim N(A) = k and dim N(B) = l. Let C be an 2 x 2 block…

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Q: A and B are n x n matrices. Check the true statements below: A. If det A is zero, then two rows or…

A: We check the given statements are true or false.

Q: Let Ao be an 5 x 5-matrix with det (40) = 3. Compute the determinant of the matrices A1, A2, A3, A4…

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Q: Compute the determinants of the matrices: 0 1 1 3 3 1 1 2 2 -1 -1 2 2 31 2 2-3-2

A:

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.