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Fixed Slit Intensity 0.8014 3.6 1.8 1.3 1.6 60 d(A) d[A] Int-f h K 1 d[A] Int-f h k )P Int-f h k 3.6840 30 0 1 2 1.3497 3 2 0 8 98920 4 1 8 2.7000 100 1 0 1.3115 10 1 0 10 .97150 <1 323 22 9 2.5190 20 1 1 1.3064 6 1 1 .96060 5 4 2.2920 3 0 0 6 1.2592 2 .95810 0 114 2.2070 20 1.2276 23 1 1 3 0 6 .95160 4 1 0 2.0779 3 2 0 2 1.2141 2 3 .93180 4 1 3 22 452251 1.8406 40 0 2 4 1.1896 1 .92060 0 4 8 1.6941 45 1 1 6 1.1632 25577 0 210 .90810 1 310 1.6367 1 2 1 1 1.1411 1 3 4 .89980 3 012 1.6033 5 1 2 2 1.1035 2 2 6 .89540 3 2 014 1.5992 10 0 1 1.0768 4 2 .87890 6 4 1 6 27 1.4859 30 2 1 1.0557 2 110 .86480 1 2 3 8 1.4538 30 3 0 1.0428 <1 1 112 .85430 35 4 0 10 1.4138 <1[1 2 5 1.0393 3 4 0 4 .84360 1 2 14 Fixed Slit Intensity 4.4 23 1.5 1.2 1.6 0.9 d(A) d[A] Int-f h K I d(A) Int-f h k d(A] Int-f h k 2.7520 13 1 1 0 1.3046 1 1 1.0176 1 0 2 2.5323 37 0 0 2 1.2958 2 1 1.0078 3 1 2.5236 100 1 1.2656 0 .99164 4 2.3242 1 1 1 1.2618 2 22 98184 325 2.3131 23 2 2 0 1.2017 .98043 12 1.9609 3 1 1 1.1964 2 .95795 1.8676 30 2 0 1.1953 <1 1 1 .94314 7 1 1.7780 1 1 2 1.1698 1 4 325 1.7117 0 22 0 1.1617 21 22 .93361 <1 4 1.6210 <1 0 1 1.1560 42221 92115 2 1.5822 10 2 0 1.1560 4 0 91816 <1 4 1.5060 20 1 1 1.1238 4 91816 <1 3 11 1.4178 10 0 2 NmN 1.1213 <1 2 .90959 1 1 1.4101 15 1 1 4 .90421 3 3 1.1092 <1 1.4058 <1 3 1 0 1.1083 <1 88847 5233 4 1.3792 6 1 1 3 1.0913 3 1 333 .88719 133 15 1.3753 14 1.0733 1 1 88719 1.3615 <1 223 22T 1.0401 <1 22 4 1.3155 <1 1.0176 1 2 3 

          Fixed Slit Intensity 0.8014 3.6 1.8 1.3 1.6 60 d(A) d[A] Int-f h K 1 d[A] Int-f h k )P Int-f h k 3.6840 30 0 1 2 1.3497 3 2 0 8 98920 4 1 8 2.7000 100 1 0 1.3115 10 1 0 10 .97150 <1 323 22 9 2.5190 20 1 1 1.3064 6 1 1 .96060 5 4 2.2920 3 0 0 6 1.2592 2 .95810 0 114 2.2070 20 1.2276 23 1 1 3 0 6 .95160 4 1 0 2.0779 3 2 0 2 1.2141 2 3 .93180 4 1 3 22 452251 1.8406 40 0 2 4 1.1896 1 .92060 0 4 8 1.6941 45 1 1 6 1.1632 25577 0 210 .90810 1 310 1.6367 1 2 1 1 1.1411 1 3 4 .89980 3 012 1.6033 5 1 2 2 1.1035 2 2 6 .89540 3 2 014 1.5992 10 0 1 1.0768 4 2 .87890 6 4 1 6 27 1.4859 30 2 1 1.0557 2 110 .86480 1 2 3 8 1.4538 30 3 0 1.0428 <1 1 112 .85430 35 4 0 10 1.4138 <1[1 2 5 1.0393 3 4 0 4 .84360 1 2 14

Fixed Slit Intensity 4.4 23 1.5 1.2 1.6 0.9 d(A) d[A] Int-f h K I d(A) Int-f h k d(A] Int-f h k 2.7520 13 1 1 0 1.3046 1 1 1.0176 1 0 2 2.5323 37 0 0 2 1.2958 2 1 1.0078 3 1 2.5236 100 1 1.2656 0 .99164 4 2.3242 1 1 1 1.2618 2 22 98184 325 2.3131 23 2 2 0 1.2017 .98043 12 1.9609 3 1 1 1.1964 2 .95795 1.8676 30 2 0 1.1953 <1 1 1 .94314 7 1 1.7780 1 1 2 1.1698 1 4 325 1.7117 0 22 0 1.1617 21 22 .93361 <1 4 1.6210 <1 0 1 1.1560 42221 92115 2 1.5822 10 2 0 1.1560 4 0 91816 <1 4 1.5060 20 1 1 1.1238 4 91816 <1 3 11 1.4178 10 0 2 NmN 1.1213 <1 2 .90959 1 1 1.4101 15 1 1 4 .90421 3 3 1.1092 <1 1.4058 <1 3 1 0 1.1083 <1 88847 5233 4 1.3792 6 1 1 3 1.0913 3 1 333 .88719 133 15 1.3753 14 1.0733 1 1 88719 1.3615 <1 223 22T 1.0401 <1 22 4 1.3155 <1 1.0176 1 2 3
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identify the elements that have the xrd patterns measured fixed slit irtensity 08014 36 18 13 16 60 da da int f h k 1 da int f h k p int f h k 36840 30 0 1 2 13497 3 2 0 8 98920 4 1 8 27000 82981

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Chemistry: Structure and Properties
Chemistry: Structure and Properties
Nivaldo Tro 2nd Edition
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Fixed Slit Intensity 0.8014 3.6 1.8 1.3 1.6 60 d(A) d[A] Int-f h K 1 d[A] Int-f h k )P Int-f h k 3.6840 30 0 1 2 1.3497 3 2 0 8 98920 4 1 8 2.7000 100 1 0 1.3115 10 1 0 10 .97150 <1 323 22 9 2.5190 20 1 1 1.3064 6 1 1 .96060 5 4 2.2920 3 0 0 6 1.2592 2 .95810 0 114 2.2070 20 1.2276 23 1 1 3 0 6 .95160 4 1 0 2.0779 3 2 0 2 1.2141 2 3 .93180 4 1 3 22 452251 1.8406 40 0 2 4 1.1896 1 .92060 0 4 8 1.6941 45 1 1 6 1.1632 25577 0 210 .90810 1 310 1.6367 1 2 1 1 1.1411 1 3 4 .89980 3 012 1.6033 5 1 2 2 1.1035 2 2 6 .89540 3 2 014 1.5992 10 0 1 1.0768 4 2 .87890 6 4 1 6 27 1.4859 30 2 1 1.0557 2 110 .86480 1 2 3 8 1.4538 30 3 0 1.0428 <1 1 112 .85430 35 4 0 10 1.4138 <1[1 2 5 1.0393 3 4 0 4 .84360 1 2 14 Fixed Slit Intensity 4.4 23 1.5 1.2 1.6 0.9 d(A) d[A] Int-f h K I d(A) Int-f h k d(A] Int-f h k 2.7520 13 1 1 0 1.3046 1 1 1.0176 1 0 2 2.5323 37 0 0 2 1.2958 2 1 1.0078 3 1 2.5236 100 1 1.2656 0 .99164 4 2.3242 1 1 1 1.2618 2 22 98184 325 2.3131 23 2 2 0 1.2017 .98043 12 1.9609 3 1 1 1.1964 2 .95795 1.8676 30 2 0 1.1953 <1 1 1 .94314 7 1 1.7780 1 1 2 1.1698 1 4 325 1.7117 0 22 0 1.1617 21 22 .93361 <1 4 1.6210 <1 0 1 1.1560 42221 92115 2 1.5822 10 2 0 1.1560 4 0 91816 <1 4 1.5060 20 1 1 1.1238 4 91816 <1 3 11 1.4178 10 0 2 NmN 1.1213 <1 2 .90959 1 1 1.4101 15 1 1 4 .90421 3 3 1.1092 <1 1.4058 <1 3 1 0 1.1083 <1 88847 5233 4 1.3792 6 1 1 3 1.0913 3 1 333 .88719 133 15 1.3753 14 1.0733 1 1 88719 1.3615 <1 223 22T 1.0401 <1 22 4 1.3155 <1 1.0176 1 2 3
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The set R2&times;2 of all 2 &times; 2 matrices form a linear space in an obvious way. For Q90. to Q92., determine whether the given subset of R2&times;2 is a linear subspace of R2&times;2. Explain thoroughly. To show it is, you have to demonstrate that all three properties in the definition of linear subspace hold. To show it is not, you only have to show that one property fails. 90. The set of all X ∈ R2&times;2 that are symmetric, namely XT = X. 91. The set of all X ∈ R2&times;2 that satisfies X[1 2; 3 4] = [1 0; 0 1]. 92. The set of all X ∈ R2&times;2 that satisfies AX − XA = [0 0; 0 0], where A is a constant 2 &times; 2 matrix. (The exact values of the entries of A don't matter.) 93. Let R3&times;3 be the linear space of all 3 &times; 3 matrices. Let W be the set of all symmetric 3 &times; 3 matrices. Then W is a linear subspace of R3&times;3. Find a basis for W and identify dim(W). For a positive integer n, define Pn as the set of all polynomials in symbol t, of degree at most n. For example, for P2, we have 2 + 5t + t2 ∈ P2, and 2 − t ∈ P2 as well. The addition and scalar multiplication of polynomials make Pn a linear space. The neutral element is the zero polynomial 0. Remark: The zero polynomial 0 is usually not assigned a degree. But sometimes it is considered of degree −∐. With that convention, then it can be thought of as having a degree ≤ n, and so is included in Pn. 94. Every p(t) ∈ P2 can be uniquely written in the form a01 + a1t + a2t2. This statement is announcing a basis A of P2, formed by 1, t, t2. (A) Therefore, what is dim(P2)? (B) What is [2 + 3t − 5t2]A? (C) What is [3 − t]A? 95. [Some Algebra] Every p(t) ∈ P2 can be uniquely written in the form b01 + b1(t − 2) + b2(t − 2)2. In this problem, let's see how this works via a concrete case. Let p(t) = 4 − 5t + 2t2. Rewrite p(t) in the form b01 + b1(t − 2) + b2(t − 2)2. (Suggestion: A convenient way to do this is to introduce the symbol u = t − 2, thus t = u + 2. Replace t by u + 2 in 4 − 5t + 2t2, which you then simplify to the form b01 + b1u + b2u2. Then replace u by t − 2 to get the answer.) 96. Every p(t) ∈ P2 can be uniquely written in the form b01 + b1(t − 2) + b2(t − 2)2. This statement is announcing a basis B of P2. Identify this basis B. 97. Find the 3 &times; 3 matrices SAB and SBA, where A and B are the two bases of P2 from Q94. and Q96.. 98. Let A and B be the bases of P2 from Q94. and Q96.. Let p(t) = 4 − 5t + 2t2 ∈ P2. (A) What is [p(t)]A? (B) Use SBA found in Q97. and [p(t)]A above to find [p(t)]B. (C) Show that the answer above is consistent with your answer in Q95.. 99. A special case of Rn is R1. Think of R as R1. So R is a 1-dimensional linear space. Define T : P2 → R as T(p(t)) = p(2). For example, T(18 − 17t + 5t2) = 18 − 17 &sdot; 2 + 5 &sdot; 22 = 4. This T is a linear transformation. In our example, if 18 − 17t + 5t2 has been written as 4 + 3(t − 2) + 5(t − 2)2, it would be much easier to see that T maps it to 4. Use the statement that every p(t) ∈ P2 can be uniquely written in the form b01 + b1(t − 2) + b2(t − 2)2 to quickly identify a basis for ker(T). (If you understand what the question is asking, no computation will be needed.) 100. Let A and B be the bases of P2 from Q94. and Q96.. Let D : P2 → P2 be the ‐differential operator‐, i.e. D(p(t)) = p'(t). (E.g., D(t2) = 2t.) (A) Find [D]A. (B) Find [D]B from [D]A via SBADASA B, using the SBA and SAB obtained in Q97.. (C) Find [D]B more directly by finding [D(1)]B, [D(t − 2)]B, [D((t − 2)2)]B, and recall that [D]B = [[D(1)]B [D(t − 2)]B [D((t − 2)2)]B]. (Note: In Calculus I, when taking the derivative of 3(t − 2)2 + 5(t − 2) + 8, simply use the Chain Rule, with t − 2 as the inner function. This would immediately give the answer as 6(t − 2) + 5.)

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Critical Values of the t-Distribution α ν 0.02 0.015 0.01 0.0075 0.005 0.0025 0.0005 1 15.894 21.205 31.821 42.433 63.656 127.321 636.578 2 4.849 5.643 6.965 8.073 9.925 14.089 31.600 3 3.482 3.896 4.541 5.047 5.841 7.453 12.924 4 2.999 3.298 3.747 4.088 4.604 5.598 8.610 5 2.757 3.003 3.365 3.634 4.032 4.773 6.869 6 2.612 2.829 3.143 3.372 3.707 4.317 5.959 7 2.517 2.715 2.998 3.203 3.499 4.029 5.408 8 2.449 2.634 2.896 3.085 3.355 3.833 5.041 9 2.398 2.574 2.821 2.998 3.250 3.690 4.781 10 2.359 2.527 2.764 2.932 3.169 3.581 4.587 11 2.328 2.491 2.718 2.879 3.106 3.497 4.437 12 2.303 2.461 2.681 2.836 3.055 3.428 4.318 13 2.282 2.436 2.650 2.801 3.012 3.372 4.221 14 2.264 2.415 2.624 2.771 2.977 3.326 4.140 15 2.249 2.397 2.602 2.746 2.947 3.286 4.073 16 2.235 2.382 2.583 2.724 2.921 3.252 4.015 17 2.224 2.368 2.567 2.706 2.898 3.222 3.965 18 2.214 2.356 2.552 2.689 2.878 3.197 3.922 19 2.205 2.346 2.539 2.674 2.861 3.174 3.883 20 2.197 2.336 2.528 2.661 2.845 3.153 3.850 21 2.189 2.328 2.518 2.649 2.831 3.135 3.819 22 2.183 2.320 2.508 2.639 2.819 3.119 3.792 23 2.177 2.313 2.500 2.629 2.807 3.104 3.768 24 2.172 2.307 2.492 2.620 2.797 3.091 3.745 25 2.167 2.301 2.485 2.612 2.787 3.078 3.725 26 2.162 2.296 2.479 2.605 2.779 3.067 3.707 27 2.158 2.291 2.473 2.598 2.771 3.057 3.689 28 2.154 2.286 2.467 2.592 2.763 3.047 3.674 29 2.150 2.282 2.462 2.586 2.756 3.038 3.660 30 2.147 2.278 2.457 2.581 2.750 3.030 3.646 40 2.123 2.250 2.423 2.542 2.704 2.971 3.551 60 2.099 2.223 2.390 2.504 2.660 2.915 3.460 120 2.076 2.196 2.358 2.468 2.617 2.860 3.373 ∞ 2.054 2.170 2.326 2.432 2.576 2.807 3.290 ν 0.02 0.015 0.01 0.0075 0.005 0.0025 0.0005 α

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Transcript

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00:01 We have been given the set of all x belonging to r2x2 that are symmetric namely xtransport is equal to x.
00:22 Now the set r2x2 of all 2x2 matrices form a linear space.
00:37 We have to determine whether the given subset of r2x2 is a linear subspace of r2x2.
00:53 Now for w to be subspace of v if for all u ,v belonging to w, au plus v belongs to w...
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