If | 2 i -3 i 1 2 3 i -1 10 3 i |=x+iy, then (x, y) is (a) (

step 1 So, in the given question we have a determinant that is given as 2i minus 3i 1, 2 3i minus 1, 10

If | 2 i -3 i 1 2 3 i -1 10 ...

If $\left|\begin{array}{ccc}2 \mathrm{i} & -3 \mathrm{i} & 1 \\ 2 & 3 \mathrm{i} & -1 \\ 10 & 3 & \mathrm{i}\end{array}\right|=\mathrm{x}+\mathrm{iy}$, then $(\mathrm{x}, \mathrm{y})$ is
(a) $(3,3)$
(b) $(2,3)$
(c) $(3,0)$
(d) $(0,0)$

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Key Concepts

Matrix Algebra

Matrix algebra involves operations on matrices including addition, multiplication, and computing determinants. When the entries of a matrix are complex numbers, the same algebraic principles apply but require complex arithmetic. This field is fundamental to understanding linear transformations, solving systems of linear equations, and other higher-level mathematical analyses.

Determinant

The determinant is a scalar value computed from the elements of a square matrix that reflects certain properties such as the volume scaling factor of the linear transformation associated with the matrix, and whether the matrix is invertible. For a 3x3 matrix, the determinant is often computed using the rule of Sarrus or cofactor expansion, and it plays a crucial role in areas such as solving systems of equations and finding eigenvalues.

Complex Numbers

Complex numbers extend the real numbers by including the imaginary unit 'i', where i^2 = -1. Operations involving complex numbers include addition, multiplication, and the handling of real and imaginary parts separately. In the context of matrix determinants, complex entries require careful arithmetic to correctly combine real and imaginary components.

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