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: 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: don't understand how the equation turned into 5x+x+6/x(x+6), could you go through the equation again…

A:

Q: -1 6 3 -8 3 1. Find an orthogonal basis for the column space of the matrix 1 -2 6 1 -4 -3

A: Gram Schmidt Orthogonalization process- Let the orthogonal basis is denoted by, {v1, v2,......} and…

Q: Find the basis for the Null space of the matrix 1 4 5 2 1 3 0 1 3 2 2 A = 2

A: A=14522130-1322 →R3→R3+R1R2→R2-2R1…

Q: 1. Show that the matrix 2 1 A = 1 2 -1 -1 is positive definite.

A: Given :- a matrix A  We need to show that a matrix is positive definite. We know that , A symmetric…

Q: Find a basis for the null space of the matrix. [10-7-2] A = 01 7-2 00 0 0

A: The given matrix is A=10-7-2017-20000. We have to find the basis for the null space of the matrix.

Q: Find a 2 x 2 matrix such that (199-41 188- 6 6 2

A:

Q: 2. Consider the following matrix and its RREF [40-8-1 6 3 3 A = 3 1 -2 4 1 1 0 0 3 -1 0 2 43 4 -2-9…

A:

Q: 7 Let y = and u Write y as the sum of two orthogonal vectors, one in 5 4 Span {u} and one orthogonal…

A: Step 1:Step 2:Step 3:Step 4:

Q: 5. Let A = 7453 7-9 -4 5 3-3 -7 6 7 -2 -6 -5 5 8 5-6 2 8-1-7-4 8 449 3 -4 5 -7 -6 -3 5 6-8-5 •…

A: Given A=7-9-453-3-7-467-2-6-555-7-65-628-358-1-7-486-8-54493. Applying row operations: Apply R1→R17:…

Q: 9. Show that the matrices (6) 65), (8), and (1) generate M2×2(F).

A: We have to show that the matrix  and  generate

Q: Four MBA students take the same six courses at graduate business school. Their final marks in these…

A:

Q: 4. Suppose B, I – B-' are invertible matrices and (X – A)- = BX-1, find X (as an expression in A,…

A: A matrix Y is said to be invertible if and only if Y-1 Y=Y Y-1=I

Q: 2. Use row operations to transform the following matrix 1 0 -1 1 012 4 in the form 001 −1 1 2 4 b…

A: Given matrix is

Q: 3) Determine whether the following matrices are diagonalizable. [6 3 -8] a) A = |0 -2 [1 3. 2 -1 01…

A:

Q: Identify the row operation that will transform the matrix 8 -9 6 1 19-50 [¹1₁ -1 4 -8 B into -1 4 -8…

A:

Q: Find the characteristic equation for the matrix A 3 0 0 A = 0 1 -1 0. 1 3 -X3 – 7X? – 16X + 12 = 0…

A: Use the method of characteristic equation to find it as in next step.

Q: of the null space and the dimension of the column space of the -6 8 12 3 -47 2 12 4 -6 6 -8 (a)…

A: We know that  rank(M) = dim( Col(M))

Q: A jungle has 400 monkeys, and it is estimated that the maximum population of the monkeys in the…

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.