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

Gujarat Board (GSEB) - STD 12 Science - Maths (GSEB - English Medium). 79 questions in this chapter.

Question types

Solution of Simultaneous Linear Equations question types

79 questions across 3 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

79
Questions
3
Question groups
5
Question types
Sample Questions

Solution of Simultaneous Linear Equations questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
The system of linear equations:
x + y + z = 2
2x + y − z = 3
3x + 2y + kz = 4
has a unique solution if
  • A
    k ≠ 0
  • B
    −1 < k < 1
  • C
    −2 < k < 2
  • ✓
    k = 0

Answer: D.

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Q 2M.C.Q (1 Marks)1 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 4M.C.Q (1 Marks)1 Mark
The system of equations:
x + y + z = 5
x + 2y + 3z = 9
x + 3y + λz = µ
has a unique solution, if
  • A
    λ = 5, µ = 13
  • ✓
    λ ≠ 5
  • C
    λ = 5, µ ≠ 13
  • D
    µ ≠ 13

Answer: B.

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Q 5M.C.Q (1 Marks)1 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 62 Marks Questions2 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 72 Marks Questions2 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 82 Marks Questions2 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 92 Marks Questions2 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 102 Marks Questions2 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 125 Marks Questions5 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 135 Marks Questions5 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 155 Marks Questions5 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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