Suppose you wish to show that the set of vectors−1235,460 −2,55−2−3,−1341 ,−4−241is linearly dependent.(a) Enter a matrixAwhich can help you show this and userrefon it.(b)?Explain how you can tell from therrefthat the vectors are linearly dependent.(c)?Give a nontrivial linear combination of the vectors which yields0. (Hint: Make a free variablenonzero.)(d)?Find a theorem in§1.7 which allows us to conclude, without doing any of the previous compu-tations, that this set must be linearly dependent.(e)?Does this set of vectors spanR4? Justify your answer.

At wind speeds above 1000 centimeters per second (cm/sec), significant sand-moving events begin to occur. wind speeds below 1000 cm/sec deposit sand and wind speeds above 1000 cm/sec move sand to new locations. the cyclic nature of wind and moving sand determines the shape and location of large dunes. at a test site, the prevailing direction of the wind did not change noticeably. however, the velocity did change. fifty-nine wind speed readings gave an average velocity of x = 1075 cm/sec. based on long-term experience, σ can be assumed to be 245 cm/sec. (a) find a 95% confidence interval for the population mean wind speed at this site. (round your answers to the nearest whole number.) lower limit cm/sec upper limit cm/sec