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Use the steps below to prove the following relations among the four fundamental subspaces determined by an m X n matrix A.
a. Show that Row A is contained in (Nul A)⊥. (Show that if x is in Row A, then x is orthogonal to every u in Nul A.)
b. Suppose rank A = r. Find dim Nul A and dim (Nul A)⊥, and then deduce from part (a) that Row A = (Nul A)⊥.
c. Explain why Col A = (Nul AT)⊥.
Linear Regression features to find the equation for V.
What to three decimal places is the principal value of [5-i8]^((8+i1)/10) real and imaginary parts - give one other value of this number finding the real part and imaginary part
A steep mountain is inclined 74 degree to the horizontal and rises 3400 ft above the surrounding plain. A cable car is to be installed that will travel from a point 910 ft from the base (along the horizontal) to the top of the mountain.
How many years are covered in each of the primary comparative financial statements and were all of these statements audited? Name the auditors. What were the auditors' conclusions concerning these statements?
Prove that f is dierentiable at x = 0 and that f (0) = 0. Hint: Write down the limit you are trying to show to prove that the derivative at 0 exists.
Refer to wage data, which reports information on annual wages for a sample of 100 workers. Also included are variables relating to industry, years of experience, and gender for each worker.
Thor has dropped his hammer, Mjolnir, into a 1ft x 1ft x 3ft container full of distilled water. If Mjonir has a uniform density of 7.8 g/cm3 and the water level was 1.5 inches lower after Thor summoned Mjolnir back to him.
A pet shop had 8 identical fish tanks in the shape of rectangular prisms. The width and height of each tank was (x - 7) inches and the length was 8 inches more than its width. The expression below shows the maximum amount of water which all the tanks..
Calculate the horizontal velocity of the cyclist at time t; this is the function x'(t). What is the horizontal velocity if θ = 20o? What is the horizontal velocity if θ = 45o?
If the number sold of franchise A is twice the number sold of franchise C, how many of each type did the company sell that year?
jack and mike have 128 marbles altogether. jack gives 14 of his marbles to norman and mike gives 37 of his to norman.
True or False: The graph of every equation of the form y = ax2 + b, where a and b are real numbers and a is not zero, is a parabola with the y-axis as the axis of symmetry.
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