7) (10) Are the following matrices linearly independent? Basis for M,? [3 6][0 -1] 3 -6 -1 1 07 and -81 -12 -4 -1 2

Q: Suppose A is a 4 × 5 matrix and the following is a basis for Nul(A). EXPLAIN why 1 0 0 122HO A- 2…

A:

Q: Find the basis of the null space of the matrix 1. A = 2 -1 3 6 6 -2 (a) , (b) (c) (d) d. a O b O…

A: Given - A = 12-136-2 To find - Find the basis of the null space of the matrix A.

Q: Consider the following matrix 1 A 8 5 -3 5 -1 -3 -1 5 (a) State whether the matrix is positive or…

A: I have used the fact that a matrix is positive definite if f all eigen values are positive

Q: Find a basis of the null space of the following matrix: A = || = 0 -9 -4 -5 -15 1 1 12 -3 3 -3 1

A: Reduced Row echelon form

Q: 0 0 -2 –2 0 -3 2 -2 -3 -3 -1 -3 -3 -1 3 -1 -2 B = 1 3 -2 -2 -2 3 -3 1 • Consider the matrix product…

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Q: What is the resulting matrix? ( 2 0 -5 ) * ( 21 -8 -31 )T

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Q: Determine whether or not the following sets S of 2 x 2 matrices are linearly independent. 2-7 -4 0…

A: Since you have posted a multiple question according to guidelines I will solve first(Q.1) question…

Q: 2 1 0 -1 3 1 Calculate the rank of the matrix P = 1 2 0 3 1 1 1 -1 - 5 -7 3 -

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Q: 16) Find the following matrix product: 2 0 1 3 0 0 1 3 2 4 2

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Q: Which of the following matrices are diagonalizable?

A: We know if the all eigenvalues of a matrix are distinct and equal  to order of the matrix .then…

Q: A, B, C are 3 x 3 matrices with det(A) = -3, det(B) = -2, det(C) = 6. What is det[(-3)A]? O 27 81 -9…

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Q: Find the characteristic polynomial of each of the follow- ing matrices: 1 2 0 1 2 17 1 (a) (b) -1 3…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 6.- For the matrices [A] g 3 -2 4 -2; [A] =-5 3 3 2 3

A: “Since you have posted multiple questions, we will solve first question for you. To get remaining…

Q: (a) Let C₁, C2, C3, and ♬ be the columns given below. Let C be the matrix C = [ ₁ ₂ 3 ]. That is, C…

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Q: Find the area of the triangle with the points A(1, 1,5), B(3, 4,3), and C(1,5, 7) by using the cross…

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you. If…

Q: -1] 2 -3 -47 4. The matrix product 4 1 20 1.

A: We need to find matrix product.

Q: Find the characteristic polynomial of the matrix

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Q: TEX Find the area under the surface z = 1+cos 4 directly above the outer rim the circle x² + y² =9…

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Q: 2. For the given matrices A find A-¹ if it exists and verify that AA-¹ = A-¹A=I. If A-¹ does not…

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Q: Q5: Write the following as a product of elementary matrices. 8 00 1 1 -2 (а) |0 -3 1 0] 0 2 0 5 0 20…

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Q: Find the orthogonal diagonalization of the following symmetric matrices. = [136] a. A =

A: A=[13  6       6    -3] Repost the next question.

Q: ind a basis for the nullspace of the matr

A: Given,         A=13-2501-12-2-64-10

Q: [1 2 3 5 6? Which of the following matrices are submatrices of A = 4 7 8. [; } 1 2 (c) 8 1 (a) 3 4…

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Q: Diagonalize the following matrix: 21 0 4 - 1 -4 3 1 - 1 400 0 1 0 00-2 not diagonalization 40 0 02 0…

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Q: (12) Use the adjoint of matrix to find the third row fourth column element of the inverse of -1 1 4)…

A: Consider the given matrix as A=0-11432-21040110-11. The inverse of the matrix A is given by…

Q: Find a non-zero 2 x 2 matrix such that 4 6 -12] 0 0 0 0 -[1 =

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Q: Is the following 2 1 1 -3 0 2 A = matrix A strictly diagonally dominant? -1 1 7

A: The given matrix .The objective is to determine whether the matrix is strictly diagonally dominant…

Q: 2, 1 0 2 0 0 0 2 0 0 0 2 Are the matrices 2 1 and similar? Yes No 0 2

A: Given matrices are  210021002 and 200020002

Q: 3. Find the QR-factorization of the following matrices (show all of your work): [1 1 (a) 2 3 (b) 1 3…

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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.