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Let A be a 3 x 3 matrix whose columns are linearly dependent (i.e. columns lie in one plane). Then consider the two statements:
(I) Any vector which is a linear combination of the columns of A lies in the same plane.
(II) The system of equation Ax = b has at least one solution for any b ∈ ℝ3 Then
- a)I is true but ll is not
- b)II is true but l is not
- c)Both I and II are true
- d)Neither I nor ll is true
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Let A be a 3 x 3 matrix whose columns are linearly dependent (i.e. col...
Given.A is a 3 x 3 matrix whose columns are linearly dependent.
⇒ Rank (A) ≤ 2
Let 
Clearly columns of A are linearly dependent
Let 
Also Ax = b does not have any solution
⇒ Statement (II) is false
Now, let 
Since columns of A are linearly dependent.
⇒ (c1, c2, c3) = a(a1, a2, a3) + b(b1, b2, b3)
⇒ (c1, c2, c3) =(aa1+bb1, aa2+bb2, aa3+bb3)
Let v be any vector which is a linear combination of column of A ie.
v = α(a1, a2, a3) + β(b1, b2, b3) + r(c1, c2, c3)
= (α + ra)(a1, a2, a3) + (β + rb)(b1, b2, b3)
⇒ v lies in the same plane
⇒ Statement (I) is true.
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Let A be a 3 x 3 matrix whose columns are linearly dependent (i.e. columns lie in one plane). Then consider the two statements:(I) Any vector which is a linear combination of the columns of A lies in the same plane.(II) The system of equation Ax = b has at least one solution for anyb ∈ 3Thena)I is true but ll is notb)II is true but l is notc)Both I and II are trued)Neither I nor ll is trueCorrect answer is option 'A'. Can you explain this answer?
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Let A be a 3 x 3 matrix whose columns are linearly dependent (i.e. columns lie in one plane). Then consider the two statements:(I) Any vector which is a linear combination of the columns of A lies in the same plane.(II) The system of equation Ax = b has at least one solution for anyb ∈ 3Thena)I is true but ll is notb)II is true but l is notc)Both I and II are trued)Neither I nor ll is trueCorrect answer is option 'A'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let A be a 3 x 3 matrix whose columns are linearly dependent (i.e. columns lie in one plane). Then consider the two statements:(I) Any vector which is a linear combination of the columns of A lies in the same plane.(II) The system of equation Ax = b has at least one solution for anyb ∈ 3Thena)I is true but ll is notb)II is true but l is notc)Both I and II are trued)Neither I nor ll is trueCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let A be a 3 x 3 matrix whose columns are linearly dependent (i.e. columns lie in one plane). Then consider the two statements:(I) Any vector which is a linear combination of the columns of A lies in the same plane.(II) The system of equation Ax = b has at least one solution for anyb ∈ 3Thena)I is true but ll is notb)II is true but l is notc)Both I and II are trued)Neither I nor ll is trueCorrect answer is option 'A'. Can you explain this answer?.
Let A be a 3 x 3 matrix whose columns are linearly dependent (i.e. columns lie in one plane). Then consider the two statements:(I) Any vector which is a linear combination of the columns of A lies in the same plane.(II) The system of equation Ax = b has at least one solution for anyb ∈ 3Thena)I is true but ll is notb)II is true but l is notc)Both I and II are trued)Neither I nor ll is trueCorrect answer is option 'A'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let A be a 3 x 3 matrix whose columns are linearly dependent (i.e. columns lie in one plane). Then consider the two statements:(I) Any vector which is a linear combination of the columns of A lies in the same plane.(II) The system of equation Ax = b has at least one solution for anyb ∈ 3Thena)I is true but ll is notb)II is true but l is notc)Both I and II are trued)Neither I nor ll is trueCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let A be a 3 x 3 matrix whose columns are linearly dependent (i.e. columns lie in one plane). Then consider the two statements:(I) Any vector which is a linear combination of the columns of A lies in the same plane.(II) The system of equation Ax = b has at least one solution for anyb ∈ 3Thena)I is true but ll is notb)II is true but l is notc)Both I and II are trued)Neither I nor ll is trueCorrect answer is option 'A'. Can you explain this answer?.
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