(p) X {(x1, 22, 3)| x1- 2-23} is orthogonal to Y = {(y1,y2, y3) 1y1+y2+2y3 T 2. Let 1, 2, 3 be linearly independent vectors in R" and let y1 x1 ax2, Y2 = x2 + X3, and y3=3+x1 Are y1, y2, 3y3 linearly independent? Prove your answer. 3. Whether the following vectors x + 2,x +1, 1 are linearly independent in P3. 1 2 3 4 2 1-3 2 3 3 0 4. Let A = 2 Find a basis of N(A),/row space of A/ column space of A. (b) Find nullity (A) and rank A. 5. Let A and B be two n xn matrices. Suppose that AB On. Show that rank A + rank B

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A: Given:- Numbers are 56 and 34  To find:- LCM of (56, 34)  Method:- i use prime Factorization method

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.