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Linear algebra and geometry
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Let and let be the matrix given in MATLAB by
A = pascal(n);
Let be the matrix obtained from by adding three zero columns. Let be the matrix obtained from by adding three rows whose entries are all .
Which of the following statements is correct?
Let the points , , in the plane be given in MATLAB by
A=[1,9,0];
B=[1,2,2];
C=[1,0,9];
The area of the quadrilateral determined by , , and is
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Let be the vectors given in MATLAB byu = [1057,1218,91];v = [-151,-174,-13];w = [-6,-5,16];Which of the following statements is correct?
Let e be vectors given in MATLAB byv = [2077/974; 1030/423; -1029/4189];w = [6129/312; -7193/9987; 2357/6478];and let be the orthogonal projection of along the direction of . Which of the following statements is correct?
Let the following vectors be given in MATLAB:
v1 = [5, -2, 3, 6, 7, -1, 8, 4];
v2 = [1, 4, -3, 9, 2, 0, 7, -5];
v3 = [2/3, 1/4, 5/2, 7/8, 3, 9/5, 1/7, 6/5];
v4 = [3, -1, 8, 5, 0, -2, 6, 9];
v5 = [4, 7, -5, 2, 1, 8, -3, 0];
Let be the matrix having these vectors as columns. How many solutions does the homogeneous system admit?
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