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The maximum value of the determinant among all 2×2 real symmetric matrices with trace 14
is ________.
is ________.
Correct answer is '49'. Can you explain this answer?
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The maximum value of the determinant among all 2×2 real symmetri...
Using maxima and minima of a function of two variables, we have f is maximum at
x = 0, y = 7 and therefore, maximum value of the determinant is 49
x = 0, y = 7 and therefore, maximum value of the determinant is 49
Most Upvoted Answer
The maximum value of the determinant among all 2×2 real symmetri...
$\times 2$ matrices with entries from $\{-1, 0, 1\}$ is $4$.
Proof: Let $A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}$ be a $2 \times 2$ matrix with entries from $\{-1, 0, 1\}$. Then we have four cases:
Case 1: $a = b = c = d = 0$. In this case, $\det A = 0$.
Case 2: Two of $a, b, c, d$ are $0$, and the other two are $\pm 1$. Without loss of generality, assume $a = b = 0$ and $c = 1$ and $d = -1$. Then $\det A = -1$.
Case 3: Three of $a, b, c, d$ are $0$, and the other one is $\pm 1$. Without loss of generality, assume $a = b = c = 0$ and $d = 1$. Then $\det A = 0$.
Case 4: Two of $a, b, c, d$ are $-1$ or $1$, and the other two are different from each other and from $\pm 1$. Without loss of generality, assume $a = b = 1$, $c = -1$, and $d = 0$. Then $\det A = 1$.
Therefore, the maximum value of the determinant among all $2 \times 2$ matrices with entries from $\{-1, 0, 1\}$ is $4$. This occurs when $A = \begin{pmatrix} 1 & 1 \\ 1 & 0 \end{pmatrix}$.
Proof: Let $A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}$ be a $2 \times 2$ matrix with entries from $\{-1, 0, 1\}$. Then we have four cases:
Case 1: $a = b = c = d = 0$. In this case, $\det A = 0$.
Case 2: Two of $a, b, c, d$ are $0$, and the other two are $\pm 1$. Without loss of generality, assume $a = b = 0$ and $c = 1$ and $d = -1$. Then $\det A = -1$.
Case 3: Three of $a, b, c, d$ are $0$, and the other one is $\pm 1$. Without loss of generality, assume $a = b = c = 0$ and $d = 1$. Then $\det A = 0$.
Case 4: Two of $a, b, c, d$ are $-1$ or $1$, and the other two are different from each other and from $\pm 1$. Without loss of generality, assume $a = b = 1$, $c = -1$, and $d = 0$. Then $\det A = 1$.
Therefore, the maximum value of the determinant among all $2 \times 2$ matrices with entries from $\{-1, 0, 1\}$ is $4$. This occurs when $A = \begin{pmatrix} 1 & 1 \\ 1 & 0 \end{pmatrix}$.
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The maximum value of the determinant among all 2×2 real symmetric matrices with trace 14is ________.Correct answer is '49'. Can you explain this answer?
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The maximum value of the determinant among all 2×2 real symmetric matrices with trace 14is ________.Correct answer is '49'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The maximum value of the determinant among all 2×2 real symmetric matrices with trace 14is ________.Correct answer is '49'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The maximum value of the determinant among all 2×2 real symmetric matrices with trace 14is ________.Correct answer is '49'. Can you explain this answer?.
The maximum value of the determinant among all 2×2 real symmetric matrices with trace 14is ________.Correct answer is '49'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The maximum value of the determinant among all 2×2 real symmetric matrices with trace 14is ________.Correct answer is '49'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The maximum value of the determinant among all 2×2 real symmetric matrices with trace 14is ________.Correct answer is '49'. Can you explain this answer?.
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