Identify the following statements as true or false.

(a) A subset H of Rn is a subspace if the zero vector is in H.
(b) Given vectors v1,..., vp, in Rn, the set of all linear combinations of these vectors is a subspace of Rn.
(c) The null space of an m x n matrix is a subspace of Rn.
(d) The column space of a matrix A is the set of solutions of Ax=b.
(e) If B is an echelon form of a matrix A, then the pivot columns of B form a basis for Col A.

/is used for a fraction 1) if x = 2/3 and y = 3/4, what is the value of (x + y) (x/y) expressed as a common fraction? 2) what is the least positive integer greater than 1 that leaves a remainder of 1 when divided by each of 2, 3, 4, 5, 6, 7, 8, and 9? 3) the ponde family's powerjet pumps 420 gallons of water per hour. at this rate, how many gallons of water will it pump in 45 minutes? 4) kim's insurance company pays 80% of the cost of all prescription medication she purchases in a year beyond the first $250 worth of prescriptions. her prescriptions for this year cost a total of $570. how many dollars of this amounts will kim's insurance company pay?

Find the arc length parameter along the given curve from the point where tequals=0 by evaluating the integral s(t)equals=integral from 0 to t startabsolutevalue bold v left parenthesis tau right parenthesis endabsolutevalue d tau∫0tv(τ) dτ. then find the length of the indicated portion of the curve r(t)equals=1010cosine tcost iplus+1010sine tsint jplus+88t k, where 0less than or equals≤tless than or equals≤startfraction pi over 3 endfraction π 3.

Evaluate the expression. (9 + 5)(3 + 2)0