Let A= pmatrix 4 & -1 2 & 3 pmatrix and Y(t)= pmatrix 2t+1 t-3 pmatrix

MATHEMATICS · Multi-part · CBSE · Mathematics · Determinants · Determinants

Problem

Let

A=\begin{pmatrix}4 & -1\\ 2 & 3\end{pmatrix}\quad\text{and}\quad Y(t)=\begin{pmatrix}2t+1\\ t-3\end{pmatrix},

where

t

is a real parameter. (i) Obtain the general solution vector

X(t)=\begin{pmatrix}x(t)\\y(t)\end{pmatrix}

of the system

AX=Y(t)

. (ii) Using the result from part (i), find the numerical values of

x

and

y

when

t=2