Determine if the columns of the matrix A = - 2 1 4 0 84 4 t 0 are linearly independent.

A = [2 -1 0 1; 3 5 7 -1; 1 4 2 7] List the row and column vectors of the matrix.

Consider the following matrix: 10 A = = 10 1 0 1 1 Explain why the columns of A are linearly dependent, but any choice of two columns from A will be linearly independent.

Let A and B be n × n matrices and assume that columns of B are linearly dependent. Show that columnsof the product AB must also be linearly dependent.

Find the change of coordinates matrix, P, from C to B if B = {b₁,b₂), C = {c₁, c₂), b₁ = (7,-2), b₂ = (2, -1), c₁ = (4,1), c2 = (5,2) O P = [a₁ a₂], a₁ = (3,-2), a₂ = (8,-5) O P = [a₁ a₂], a₁ = (8,-5), a2 = (3,-2) ○ P = [a₁ a₂], a₁ = (2,-5), a₂ = (3,-8) OP [a1 a2], a₁ = = (3,-8), a2 = (2,-5) O P = [a₁ a₂], a₁ = (-3,2), a₂ = (-8, 5)

Q2.Find the rank of the matrix B. r1 -1 3- 4 B= 3 1 1 -1 1 1

Find a non-zero vector V in the row space of the matrix -20 4 -9 -3 12 25 --5 -12 -4 16 V

Determine the matrix if it is a linear combination of a b 3 11 [-1 5 9 4 1 3 4 6 11 A. a = 5; b = -7 B. a = 5; b = 7 C. a = 7; b = 5 D. a = -5 ; b = 7

Find all a andB >0 so that the matrix B 28 6 2 is 2 diagonally dominant;

Use a software program or a graphing utility with matrix capabilities to write v as a linear combination of u,, u,, uz, u4, and u.. Then verify your solution. v = (5, 8, 7, -2, 4) u1 = (1, 1, –1, 2, 1) uz = (2, 1, 2, -1, 1) uz = (1, 2, 0, 1, 2) u4 = (0, 2, 0, 1, -4) u5 = (1, 1, 2, -1, 2) V =