#Q58 Let D be a non-zero nรn real matrix with nโฅ2. Which of the following implications is valid?
Anonymous Quiz
18%
detโก(D)=0 implies rank (D)=0
44%
detโก(D)=1 implies rank (D)โ 1
27%
rank (D)=1 implies detโก(D)โ 0
11%
rank (D)=n implies detโก(D)โ 1
#Q59 Let A,B be nรn real matrices. Which of the following statements is correct ?
Anonymous Quiz
12%
Rank (A+B)=rank(A)+rank (B)
53%
Rank (A+B)โคrank(A)+rank (B)
23%
Rank (A+B)=minโก{rank(A),rank (B)}
12%
Rank (A+B)=maxโก{rank(A),rank (B)}
#Q60 The row space of a 20ร50 matrix A has dimension 13. What is the dimension of the space of solutions of Ax=0?
Anonymous Quiz
17%
7
27%
13
16%
33
40%
37
โค2
#Q61 Let A be a mรn matrix of rank n with real entries. Choose the correct statement
Anonymous Quiz
17%
Ax = b has a solution for any b
13%
Ax = 0 does not have a solution
60%
If Ax = b has a solution, then it is unique
10%
y'A=0 for some non-zero y, where y'denotes the transpose of the vector y
#Q62 Let A be an nรm matrix with each entry equal to +1,-1 or 0 such that every column has exactly one +1 and exactly one โ 1 . We can conclude that
Anonymous Quiz
45%
Rank A โค n - 1
27%
Rank A = m
13%
n โค m
15%
n - 1 โค m
#Q63 Let A be (m ร n) matrix and B be a (n ร m)matrix over real numbers with m < n. Then
Anonymous Quiz
25%
AB is always non-singular
30%
AB is always singular
20%
BA is always non-singular
24%
BA is always singular
#Q64 Let A and B be 2 X 2 matrices. Then which of the following is true ?
Anonymous Quiz
15%
det(A+B) + det (A-B) = det A + detB
35%
det(A+B) + det(A-B) = 2detA - 2 det B
43%
det (A+B) + det(A-B) = 2detA + 2detB
8%
det(A+B) - det(A-B) = 2detA โ 2detB
โค1
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๐๐๐ฒ ๐๐ | ๐๐ข๐ฆ๐๐ง๐ฌ๐ข๐จ๐ง ๐จ๐ ๐ฅ๐ข๐ง๐๐๐ซ ๐๐ฉ๐๐ง| ๐๐ข๐ง๐๐๐ซ ๐๐ฅ๐ ๐๐๐ซ๐
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๐๐ก๐๐ฒ ๐ฐ๐๐ซ๐ ๐จ๐ง๐๐ ๐ข๐ง ๐ฒ๐จ๐ฎ๐ซ ๐๐ฑ๐๐๐ญ ๐ฉ๐จ๐ฌ๐ข๐ญ๐ข๐จ๐ง. ๐๐ก๐๐ฒ ๐๐๐๐๐ฉ๐ญ๐๐ ๐ญ๐ก๐ ๐๐ก๐๐ฅ๐ฅ๐๐ง๐ ๐. ๐๐ก๐๐ฒ ๐ฌ๐ฎ๐๐๐๐๐๐๐. ๐๐ก๐ ๐จ๐ง๐ฅ๐ฒ ๐ช๐ฎ๐๐ฌ๐ญ๐ข๐จ๐ง ๐ข๐ฌ: ๐๐ข๐ฅ๐ฅ ๐ฒ๐จ๐ฎ?
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L04 | Ordinary Differential Equations | Top 500 Most Probable Questions
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๐๐๐ฒ ๐๐|๐๐ซ๐๐๐ซ ๐จ๐ ๐๐ซ๐จ๐ฎ๐ฉ | ๐๐ซ๐จ๐ฎ๐ฉ ๐๐ก๐๐จ๐ซ๐ฒ
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