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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Transform [1243-15246] into an upper triangular matrix by using suitable row transformations - Mathematics and Statistics

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प्रश्न

Transform `[(1, 2, 4),(3, -1, 5),(2, 4, 6)]` into an upper triangular matrix by using suitable row transformations

बेरीज
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उत्तर

Let A = `[(1, 2, 4),(3, -1, 5),(2, 4, 6)]`

Applying R2 → R2 – 3R1 and R3 → R3 – 2R1, we get

`[(1, 2, 4),(0, -7, -7),(0, 0, -2)]`

This is required upper triangular matrix.

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पाठ 1.2: Matrics - Short Answers I

संबंधित प्रश्‍न

Let A be a nonsingular square matrix of order 3 × 3. Then |adj A| is equal to ______.


Examine the consistency of the system of equations.

2x − y = 5

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5x − 2y + 6z = −1


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4x – 3y = 3

3x – 5y = 7


If \[A = \begin{bmatrix}2 & 5 \\ 2 & 1\end{bmatrix} \text{ and } B = \begin{bmatrix}4 & - 3 \\ 2 & 5\end{bmatrix}\] , verify that |AB| = |A| |B|.

 

Find the value of x, if

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Without expanding, show that the value of the following determinant is zero:

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2y − 3z = 0
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If A is a singular matrix, then write the value of |A|.

 

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Evaluate \[\begin{vmatrix}4785 & 4787 \\ 4789 & 4791\end{vmatrix}\]


If I3 denotes identity matrix of order 3 × 3, write the value of its determinant.


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Evaluate: \[\begin{vmatrix}\cos 15^\circ & \sin 15^\circ \\ \sin 75^\circ & \cos 75^\circ\end{vmatrix}\]


Find the maximum value of \[\begin{vmatrix}1 & 1 & 1 \\ 1 & 1 + \sin \theta & 1 \\ 1 & 1 & 1 + \cos \theta\end{vmatrix}\]


The value of \[\begin{vmatrix}5^2 & 5^3 & 5^4 \\ 5^3 & 5^4 & 5^5 \\ 5^4 & 5^5 & 5^6\end{vmatrix}\]

 


If \[\begin{vmatrix}2x & 5 \\ 8 & x\end{vmatrix} = \begin{vmatrix}6 & - 2 \\ 7 & 3\end{vmatrix}\] , then x = 

 


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Solve the following system of equations by matrix method:
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Solve the following system of equations by matrix method:
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