Question:
The transformation 'orthogonal projection on X- axis' is given by matrix
The transformation 'orthogonal projection on X- axis' is given by matrix
Updated On: Jul 7, 2022
- $ \begin{bmatrix}0&1\\ 0&0\end{bmatrix}$
- $ \begin{bmatrix}0& 0 \\ 1 &0\end{bmatrix}$
- $ \begin{bmatrix} 1 &0 \\ 0&0\end{bmatrix}$
- $ \begin{bmatrix}0& 0 \\ 0 & 1\end{bmatrix}$
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The Correct Option is C
Solution and Explanation
Under the given transformation, a point (x, y) is transformed to (x, 0), i.e., the foot of perpendicular from (x, y) on the x-axis.
Now $x = 1x + 0y$ and $0 = 0x + 0y$, therefore, the required matrix of the transformation is $ \begin{bmatrix} 1 & 0 \\ 0&0\end{bmatrix}$
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Concepts Used:
Matrices
Matrix:
A matrix is a rectangular array of numbers, variables, symbols, or expressions that are defined for the operations like subtraction, addition, and multiplications. The size of a matrix is determined by the number of rows and columns in the matrix.
The basic operations that can be performed on matrices are:
- Addition of Matrices - The addition of matrices addition can only be possible if the number of rows and columns of both the matrices are the same.
- Subtraction of Matrices - Matrices subtraction is also possible only if the number of rows and columns of both the matrices are the same.
- Scalar Multiplication - The product of a matrix A with any number 'c' is obtained by multiplying every entry of the matrix A by c, is called scalar multiplication.
- Multiplication of Matrices - Matrices multiplication is defined only if the number of columns in the first matrix and rows in the second matrix are equal.
- Transpose of Matrices - Interchanging of rows and columns is known as the transpose of matrices.