Solution of Simultaneous Linear Equations - Maharashtra Board STD 12 Maths Questions

Q 1MCQ1 Mark

The system of linear equations:
$x + y + z = 2$
$2x + y − z = 3$
$3x + 2y + kz = 4$
has a unique solution if

✓
$k ≠ 0$
B
$−1 < k < 1$
C
$−2 < k < 2$
D
$k = 0$

Answer: A.

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Q 2MCQ1 Mark

The number of solutions of the system of equations:
$2x + y − z = 7$
$x − 3y + 2z = 1$
$x + 4y − 3z = 5$

A
$3$
B
$2$
C
$1$
✓
$0$

Answer: D.

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Q 3MCQ1 Mark

The number of solutions of the system of equations
$2x + y − z = 7$
$x − 3y + 2z = 1$
$x + 4y − 3z = 5$

A
$3$
B
$2$
C
$1$
✓
$0$

Answer: D.

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Q 4MCQ1 Mark

The system of equations:
$x + y + z = 5$
$x + 2y + 3z = 9$
$x + 3y + \lambda z = µ$
has a unique solution, if

A
$\lambda = 5, µ = 13$
✓
$\lambda \neq 5$
C
$\lambda = 5, µ \neq 13$
D
$µ \neq 13$

Answer: B.

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Q 5MCQ1 Mark

Consider the system of equations:
$a_1x + b_1y + c_1z = 0$
$a_2x + b_2y + c_2z = 0$
$a_3x + b_3y + c_3z = 0,$
if $\begin{vmatrix}\text{a}_1&\text{b}_1&\text{c}_1\\\text{a}_2&\text{b}_2&\text{c}_2\\\text{a}_3&\text{b}_3&\text{c}_3\end{vmatrix}=0$, then the system has

✓
More than two solutions.
B
One trivial and one non$-$trivial solutions.
C
No solutions.
D
Only trivial solution $(0, 0, 0)$.

Answer: A.

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Q 6Solve the Following Question.(2 Marks)2 Marks

If $\begin{bmatrix}1&0&0\\0&0&1\\0&1&0\end{bmatrix}\begin{bmatrix}\text{x}\\\text{y}\\\text{z}\end{bmatrix}=\begin{bmatrix}2\\-1\\3\end{bmatrix}$, find x, y, z.

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Q 7Solve the Following Question.(2 Marks)2 Marks

If $\begin{bmatrix}1&0&0\\0&\text{y}&0\\0&0&1\end{bmatrix}\begin{bmatrix}\text{x}\\-1\\\text{z}\end{bmatrix}=\begin{bmatrix}1\\0\\1\end{bmatrix}$, find x, y and z.

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Q 8Solve the Following Question.(2 Marks)2 Marks

If $\begin{bmatrix}1&0&0\\0&-1&0\\0&0&-1\end{bmatrix}\begin{bmatrix}\text{x}\\\text{y}\\\text{z}\end{bmatrix}=\begin{bmatrix}1\\0\\1\end{bmatrix}$, find x, y and z.

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Q 9Solve the Following Question.(2 Marks)2 Marks

If $\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}\begin{bmatrix}\text{x}\\\text{y}\\\text{z}\end{bmatrix}=\begin{bmatrix}1\\-1\\0\end{bmatrix}$, find x, y and z.

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Q 10Solve the Following Question.(2 Marks)2 Marks

If $\text{A}=\begin{bmatrix}2&4\\4&3\end{bmatrix},\text{X}=\begin{bmatrix}\text{n}\\1\end{bmatrix},\text{B}=\begin{bmatrix}8\\11\end{bmatrix}$and AX = B, then find n.

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Q 11Solve the Following Question.(5 Marks)5 Marks

Solve the following system of equations by matrix method:
$3x + 4y + 7z = 14$
$2x - y + 3z = 4$
$x + 2y - 3z = 0$

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Q 12Solve the Following Question.(5 Marks)5 Marks

Two schools P and Q want to award their selected students on the values of Tolerance, Kindness and Leadership. The school P wants to award ₹ x each, ₹ y each and ₹ z each for the three respective values to 3, 2 and 1 students respectively with a total award money of ₹ 2,200. School Q wants to spend ₹ 3,100 to award its 4, 1 and 3 students on the respective values (by giving the same award money to the three values as school P). If the total amount of award for one prize on each values is ₹ 1,200, using matrices, find the award money for each value.
Apart from these three values, suggest one more value which should be considered for award.

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Q 13Solve the Following Question.(5 Marks)5 Marks

Find $A^{-1},$ If $\text{A}=\begin{bmatrix}1&2&5\\ 1&-1&-1\\ 2&3&-1\end{bmatrix}$. Hence solve the follwing system of linear equations:
$x + 2y +5z = 10, x- y - z = - 2, 2x + 3y - z = - 11$

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Q 14Solve the Following Question.(5 Marks)5 Marks

Show that the following system of linear equations is consistent and also find solution:
$x + y + z = 6$
$x + 2y + 3z = 14$
$x + 4y + 7z = 30$

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Q 15Solve the Following Question.(5 Marks)5 Marks

If $\text{A}=\begin{bmatrix}1&-1&0\\ 2&3&4\\ 0&1&2\end{bmatrix}\text{and }\text{B}=\begin{bmatrix}2&2&-4\\ -4&2&-4\\ 2&-1&5\end{bmatrix}$ are two square matrices, find AB and hence solve the system of linear equations:
x - y = 3, 2x + 3y + 4z = 17, y + 2z = 7

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Solution of Simultaneous Linear Equations question types

Solution of Simultaneous Linear Equations questions

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Solution of Simultaneous Linear Equations Maths - Solution of Simultaneous Linear Equations

Solution of Simultaneous Linear Equations question types

Solution of Simultaneous Linear Equations questions

Generate a Solution of Simultaneous Linear Equations paper free