Algebra

Matrices & Determinants

Easy

Manjeet wants to donate a rectangular plot of land for a school in his village. When he has asked to give dimensions of the plot, he told that if its length is decreased by 50 m and breadth is increased by 50 m, then its area will remain same, but if its length is decreased by 10 m and breadth is decreased by 20 m, then its area will decrease by 5300 $m^2$ . If length and breadth of the plot are $x$ and $y$ respectively, then based on above information answer the question.

The linear equation involving $x$ and $y$ are written in matrix form as:

$\begin{bmatrix} 1 & -1 \\ 2 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 50 \\ 550 \end{bmatrix}$

$\begin{bmatrix} 1 & 1 \\ 2 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 50 \\ 550 \end{bmatrix}$

$\begin{bmatrix} 1 & 1 \\ 2 & -1 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 50 \\ 550 \end{bmatrix}$

$\begin{bmatrix} 1 & 1 \\ 2 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} -50 \\ -550 \end{bmatrix}$

✅ Correct Option: 1

From the equations $x - y = 50$ and $2x + y = 550$ , the coefficient matrix has rows $(1, -1)$ and $(2, 1)$ , with constants $(50, 550)$ . So the matrix form is $\begin{bmatrix} 1 & -1 \\ 2 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 50 \\ 550 \end{bmatrix}$ .

Question 46

The length ( $x$ ) and breadth ( $y$ ) of plot satisfy equations:

Question 48

The length of the plot is:

Question 49

The breadth of plot is:

Question 50

Area of the rectangular plot is:

The linear equation involving xxx and yyy are written in matrix form as:

Solution

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Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

The linear equation involving $x$ and $y$ are written in matrix form as: