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Let M and N be two 3 × 3 matrices such that MN = NM. Further, if M ≠ N2 and M2 = N4, then
- a)determinant of (M2 + MN2) is 0
- b)there is 3 × 3 non-zero matrix U such that (M2 + MN2)U is the zero matrix
- c)determinant of (M2 + MN2) > 1
- d)for a 3 × 3 matrix U, if (M2 + MN2)U equals the zero matrix then U is the zero matrix
Correct answer is option 'A,B'. Can you explain this answer?
Verified Answer
Let M and N be two 3 × 3 matrices such that MN = NM. Further, if...
Given MN = NM, M ≠ N2 and M2 = N4.
Then M2 = N4 ⇒ (M + N2) (M – N 2) = 0
⇒ (i) M + N2 = 0 and M – N2 ≠ 0
(ii) |M + N2| = 0 and |M – N2| = 0
In each case |M + N2| = 0
∴ |M2 + MN2| = |M| |M + N2| = 0
∴ (a) is correct and (c) is not correct.
Also we know if |A| = 0, then there can be many matrices U, such that AU = 0
∴ (M2 + MN2)U = 0 will be true for many values of U.
Hence (b) is correct.
Again if AX = 0 and |A| = 0, then X can be non-zero.
∴ (d) is not correct.
Then M2 = N4 ⇒ (M + N2) (M – N 2) = 0
⇒ (i) M + N2 = 0 and M – N2 ≠ 0
(ii) |M + N2| = 0 and |M – N2| = 0
In each case |M + N2| = 0
∴ |M2 + MN2| = |M| |M + N2| = 0
∴ (a) is correct and (c) is not correct.
Also we know if |A| = 0, then there can be many matrices U, such that AU = 0
∴ (M2 + MN2)U = 0 will be true for many values of U.
Hence (b) is correct.
Again if AX = 0 and |A| = 0, then X can be non-zero.
∴ (d) is not correct.
Most Upvoted Answer
Let M and N be two 3 × 3 matrices such that MN = NM. Further, if...
X 3 matrices. Then their product MN is defined if and only if the number of columns of M is equal to the number of rows of N.
In other words, if M is a 3 x k matrix and N is a k x 3 matrix, then their product MN is defined and is a 3 x 3 matrix.
The entry in the i-th row and j-th column of the product MN is obtained by multiplying the i-th row of M by the j-th column of N, and adding up the products.
For example, if
M = [1 2 3
4 5 6
7 8 9]
and
N = [2 1 0
1 2 1
0 1 2]
then their product MN is defined and is given by
MN = [5 8 11
14 20 26
23 32 41]
In other words, if M is a 3 x k matrix and N is a k x 3 matrix, then their product MN is defined and is a 3 x 3 matrix.
The entry in the i-th row and j-th column of the product MN is obtained by multiplying the i-th row of M by the j-th column of N, and adding up the products.
For example, if
M = [1 2 3
4 5 6
7 8 9]
and
N = [2 1 0
1 2 1
0 1 2]
then their product MN is defined and is given by
MN = [5 8 11
14 20 26
23 32 41]
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Let M and N be two 3 × 3 matrices such that MN = NM. Further, if M ≠N2 and M2 = N4, thena)determinant of (M2 + MN2) is 0b)there is 3 × 3 non-zero matrix U such that (M2 + MN2)U is the zero matrixc)determinant of (M2 + MN2) > 1d)for a 3 × 3 matrix U, if (M2 + MN2)U equals the zero matrix then U is the zero matrixCorrect answer is option 'A,B'. Can you explain this answer?
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Let M and N be two 3 × 3 matrices such that MN = NM. Further, if M ≠N2 and M2 = N4, thena)determinant of (M2 + MN2) is 0b)there is 3 × 3 non-zero matrix U such that (M2 + MN2)U is the zero matrixc)determinant of (M2 + MN2) > 1d)for a 3 × 3 matrix U, if (M2 + MN2)U equals the zero matrix then U is the zero matrixCorrect answer is option 'A,B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let M and N be two 3 × 3 matrices such that MN = NM. Further, if M ≠N2 and M2 = N4, thena)determinant of (M2 + MN2) is 0b)there is 3 × 3 non-zero matrix U such that (M2 + MN2)U is the zero matrixc)determinant of (M2 + MN2) > 1d)for a 3 × 3 matrix U, if (M2 + MN2)U equals the zero matrix then U is the zero matrixCorrect answer is option 'A,B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let M and N be two 3 × 3 matrices such that MN = NM. Further, if M ≠N2 and M2 = N4, thena)determinant of (M2 + MN2) is 0b)there is 3 × 3 non-zero matrix U such that (M2 + MN2)U is the zero matrixc)determinant of (M2 + MN2) > 1d)for a 3 × 3 matrix U, if (M2 + MN2)U equals the zero matrix then U is the zero matrixCorrect answer is option 'A,B'. Can you explain this answer?.
Let M and N be two 3 × 3 matrices such that MN = NM. Further, if M ≠N2 and M2 = N4, thena)determinant of (M2 + MN2) is 0b)there is 3 × 3 non-zero matrix U such that (M2 + MN2)U is the zero matrixc)determinant of (M2 + MN2) > 1d)for a 3 × 3 matrix U, if (M2 + MN2)U equals the zero matrix then U is the zero matrixCorrect answer is option 'A,B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let M and N be two 3 × 3 matrices such that MN = NM. Further, if M ≠N2 and M2 = N4, thena)determinant of (M2 + MN2) is 0b)there is 3 × 3 non-zero matrix U such that (M2 + MN2)U is the zero matrixc)determinant of (M2 + MN2) > 1d)for a 3 × 3 matrix U, if (M2 + MN2)U equals the zero matrix then U is the zero matrixCorrect answer is option 'A,B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let M and N be two 3 × 3 matrices such that MN = NM. Further, if M ≠N2 and M2 = N4, thena)determinant of (M2 + MN2) is 0b)there is 3 × 3 non-zero matrix U such that (M2 + MN2)U is the zero matrixc)determinant of (M2 + MN2) > 1d)for a 3 × 3 matrix U, if (M2 + MN2)U equals the zero matrix then U is the zero matrixCorrect answer is option 'A,B'. Can you explain this answer?.
Solutions for Let M and N be two 3 × 3 matrices such that MN = NM. Further, if M ≠N2 and M2 = N4, thena)determinant of (M2 + MN2) is 0b)there is 3 × 3 non-zero matrix U such that (M2 + MN2)U is the zero matrixc)determinant of (M2 + MN2) > 1d)for a 3 × 3 matrix U, if (M2 + MN2)U equals the zero matrix then U is the zero matrixCorrect answer is option 'A,B'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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Let M and N be two 3 × 3 matrices such that MN = NM. Further, if M ≠N2 and M2 = N4, thena)determinant of (M2 + MN2) is 0b)there is 3 × 3 non-zero matrix U such that (M2 + MN2)U is the zero matrixc)determinant of (M2 + MN2) > 1d)for a 3 × 3 matrix U, if (M2 + MN2)U equals the zero matrix then U is the zero matrixCorrect answer is option 'A,B'. Can you explain this answer?, a detailed solution for Let M and N be two 3 × 3 matrices such that MN = NM. Further, if M ≠N2 and M2 = N4, thena)determinant of (M2 + MN2) is 0b)there is 3 × 3 non-zero matrix U such that (M2 + MN2)U is the zero matrixc)determinant of (M2 + MN2) > 1d)for a 3 × 3 matrix U, if (M2 + MN2)U equals the zero matrix then U is the zero matrixCorrect answer is option 'A,B'. Can you explain this answer? has been provided alongside types of Let M and N be two 3 × 3 matrices such that MN = NM. Further, if M ≠N2 and M2 = N4, thena)determinant of (M2 + MN2) is 0b)there is 3 × 3 non-zero matrix U such that (M2 + MN2)U is the zero matrixc)determinant of (M2 + MN2) > 1d)for a 3 × 3 matrix U, if (M2 + MN2)U equals the zero matrix then U is the zero matrixCorrect answer is option 'A,B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let M and N be two 3 × 3 matrices such that MN = NM. Further, if M ≠N2 and M2 = N4, thena)determinant of (M2 + MN2) is 0b)there is 3 × 3 non-zero matrix U such that (M2 + MN2)U is the zero matrixc)determinant of (M2 + MN2) > 1d)for a 3 × 3 matrix U, if (M2 + MN2)U equals the zero matrix then U is the zero matrixCorrect answer is option 'A,B'. Can you explain this answer? tests, examples and also practice JEE tests.
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