3. (a) Let S be the subspace of R3 spanned by the vectors x (x,x2, x3) and y = (Vi,y2, ya) Let A = У У2 Уз Show that S N(A). (b) Find the orthogonal complement of the subspace of R3 spanned by (1,2,1) and (1,-1,2)

Consider the vectors u₁ = [1,0,−1], _U2 = [1,0,0] and u3 = [0, 1, 1], v = [5, 1, 3] and w = = [1,0,3]. (a) Show that the vectors u₁, u₂ and u3 are linearly independent. (b) Show that the vector v is in the span of u₁, U₂ and u3. (c) Find the coordinate vector of v with respect to {U₁, U2, U3}. (d) Write the zero vector as as a non-trivial linear combination of the vectors u₁, U2, U3 and w.

Construction and building inspectors ensure that construction meets local and national buillding codes and ordinances, zoning regulations, and contract specifications. They spend considerable time inspecting worksites, alone or as part of a team. Most work full time during regular business hours. Many states and local jurisdictions require some type of license or certification. The median annual wage was $56,040 in May 2014. SOURCE: Bureau of Labor and Statistics, U.S. Department of Labor, Occupational Outlook Handbook, 2016 - 2017 Edition E, Construction and Building Inspectors A wheelchalir ramp with a length of 614 Inches has a horizontal distance of 610 Inches. What is the ramp's vertical distance (height)? inches State your response to the nearest 0. 1 Construction laws are very specific when it comes to access ramps for the disabled. Every vertical rise of 1 inch requires a horizontal run of at least 12 inches. Does the ramp above satisfy the requirement? O Yes O No

I know the basis converted to orthogonal is {<2, 1, -1, 1>,<11, -12, 5, -5>,<-1, -3, 0, 5>} and that the magnitude of these will be sqrt(7), sqrt(315), sqrt(35) - but I'm not sure how to use these to convert the basis to orthonormal.

Find a basis for the two-dimensional subspace of R^4 defined by