Matrics - Maharashtra Board STD 12 Science Maths Questions

Q 1Solve the Following Question.(2 Marks)2 Marks

Find the inverse of the matrix $\left[\begin{array}{cc}2 & -3 \\ -1 & 2\end{array}\right]$

Q 2Solve the Following Question.(2 Marks)2 Marks

The inverse of the matrix $\left[\begin{array}{ccc}2 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{array}\right]$ is

A
$\left[\begin{array}{ccc}\frac{1}{2} & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\end{array}\right]$
B
$\left[\begin{array}{ccc}-\frac{1}{2} & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1\end{array}\right]$
C
$\left[\begin{array}{ccc}-1 & 0 & 0 \\ 0 & -\frac{1}{2} & 0 \\ 0 & 0 & \frac{1}{2}\end{array}\right]$
D
$-\frac{1}{2}\left[\begin{array}{ccc}-\frac{1}{2} & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{array}\right]$

Q 3Solve the Following Question.(2 Marks)2 Marks

If $A=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]$ and $A X=I$, then find $X$ by using elementary transformations.

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Q 4Solve the Following Question.(2 Marks)2 Marks

Find the cofactors of the elements for the matrix $\left[\begin{array}{ll}-1 & 2 \\ -3 & 4\end{array}\right]$

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Q 5Solve the Following Question.(2 Marks)2 Marks

Find the matrix of co-factors for the matrix $\left[\begin{array}{cc}1 & 3 \\ 4 & -1\end{array}\right]$

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Q 6Solve the Following Question.(3 Marks)3 Marks

If $A^{-1}=\frac{1}{3}\left[\begin{array}{ccc}1 & 4 & -2 \\ -2 & -5 & 4 \\ 1 & -2 & 1\end{array}\right]$ and $|A|=3$, then (adj. $\left.A\right)=\ldots$.

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Q 7Solve the Following Question.(3 Marks)3 Marks

Express the following equations in matrix form and solve them by the method of reduction: $x+y+z=6,3 x-y+3 z=6$ and $5 x+5 y-4 z=3$.

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Q 8Solve the Following Question.(3 Marks)3 Marks

Find the inverse of the matrix $A$ where $A=\left[\begin{array}{lll}3 & 2 & 6 \\ 1 & 1 & 2 \\ 2 & 2 & 5\end{array}\right]$ by using adjoint method.

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Q 9Solve the Following Question.(4 Marks)4 Marks

The cost of $4$ pencils, $3$ pens and $2$ erasers is $₹ 60$ . The cost of $2$ pencils, $4$ pens and $6$ erasers is $₹ 90$ . Whereas the cost of $6$ pencils, $2$ pens and $3$ erasers is $₹ 70$ . Find the cost of each item by using matrix inversion method.

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Q 10Solve the Following Question.(4 Marks)4 Marks

Find the inverse of the matrix, $A=\left[\begin{array}{lll}1 & 3 & 3 \\ 1 & 4 & 3 \\ 1 & 3 & 4\end{array}\right]$ by using column transformations.

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Q 11Solve the Following Question.(4 Marks)4 Marks

The cost of $2$ books, $6$ notebooks and $3$ pens is $₹ 40$ . The cost of $3$ books, $4$ notebooks and $2$ pens is $₹ 35$ , while the cost of $5$ books, $7$ notebooks and $4$ pens is $₹ 61$ . Using this information and matrix method, find the cost of $1$ book, $1$ notebook and $1$ pen separately.

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Q 12Solve the Following Question.(4 Marks)4 Marks

Solve the following system of equations by the method of inversion. $x-y+z=4,2 x+y-3 z=0, x+y+z=2$

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Q 13Solve the Following Question.(4 Marks)4 Marks

If three numbers are added, their sum is $2.$ If two times the second number is subtracted from the sum of first and third numbers we get $8$ and if three times the first number is added to the sum of second and third numbers we get $4.$ Find the numbers using matrices.

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