Question Two Consider the following statements: a) A matrix Amxn is nonsingular ar b) Amxn is square c) Amxn has linear independence d) The rank of Am×n is r(A) = min{m, n} Use "necessary condition”, “sufficient condition”, or “necessary and sufficient condition” to describe how Statement a) is related to Statements b), c), and d). Here are the conditions • Necessary Condition: q constitutes a necessary condition of p; mathematically, pq, read as: if p, then q; or, p implies q • Sufficient Condition: q is a sufficient condition for p; mathematically, p = q, read as: p if q; or, if q, then p; or, q implies p • Necessary and Sufficient Condition: q is both necessary and sufficient for p; mathematically, pq, read as: p if and only if q
Question Two Consider the following statements: a) A matrix Amxn is nonsingular ar b) Amxn is square c) Amxn has linear independence d) The rank of Am×n is r(A) = min{m, n} Use "necessary condition”, “sufficient condition”, or “necessary and sufficient condition” to describe how Statement a) is related to Statements b), c), and d). Here are the conditions • Necessary Condition: q constitutes a necessary condition of p; mathematically, pq, read as: if p, then q; or, p implies q • Sufficient Condition: q is a sufficient condition for p; mathematically, p = q, read as: p if q; or, if q, then p; or, q implies p • Necessary and Sufficient Condition: q is both necessary and sufficient for p; mathematically, pq, read as: p if and only if q
Chapter2: Mathematics For Microeconomics
Section: Chapter Questions
Problem 2.6P
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Transcribed Image Text:Question Two Consider the following statements:
a) A matrix Amxn is nonsingular ar
b) Amxn is square
c) Amxn has linear independence
d) The rank of Am×n is r(A) = min{m, n}
Use "necessary condition”, “sufficient condition”, or “necessary and sufficient condition” to
describe how Statement a) is related to Statements b), c), and d).
Here are the conditions
•
Necessary Condition: q constitutes a necessary condition of p; mathematically,
pq, read as: if p, then q; or, p implies q
• Sufficient Condition: q is a sufficient condition for p; mathematically, p = q,
read as: p if q; or, if q, then p; or, q implies p
• Necessary and Sufficient Condition: q is both necessary and sufficient for p;
mathematically, pq, read as: p if and only if q
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