- 3 30 Points For Each Set Of Vectors S In The Vector Space V Decide Which Category S Fits Into I S Is Linearly Inde 1 (49.77 KiB) Viewed 37 times
3. (30 points) For each set of vectors S in the vector space V, decide which category S fits into: I. S is linearly inde
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3. (30 points) For each set of vectors S in the vector space V, decide which category S fits into: I. S is linearly inde
3. (30 points) For each set of vectors S in the vector space V, decide which category S fits into: I. S is linearly independent and spans V II. S is linearly independent but does not span V III. S is linearly dependent and spans V IV. S is linearly dependent and does not spanV (a) V=R3,S=⎩⎨⎧⎝⎛10−1⎠⎞,⎝⎛251⎠⎞,⎝⎛45−1⎠⎞⎭⎬⎫. (b) V=P3(R),S={x3+1,x2−x,x+1} (c) V=R3,S=⎩⎨⎧v1=⎝⎛125⎠⎞,v2=⎝⎛1−1−1⎠⎞,v3=⎝⎛101⎠⎞,v4=⎝⎛5−21⎠⎞⎭⎬⎫
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