If $[\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}] [\begin{matrix} 3 & 1 \\ 2 & 5 \end{matrix}] = [\begin{matrix} 7 & 11 \\ k & 23 \end{matrix}]$ , then write the value of k.

Solution

$Given [\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}] = [\begin{matrix} 3 & 1 \\ 2 & 5 \end{matrix}] = [\begin{matrix} 7 & 11 \\ k & 23 \end{matrix}]$

Now using matrix multiplication in L.H.S., we get

$[\begin{matrix} 1 x 3 + 2 x 2 & 1 x 1 + 2 x 5 \\ 3 x 3 + 4 x 2 & 3 x 1 + 4 x 5 \end{matrix}] = [\begin{matrix} 7 & 11 \\ k & 23 \end{matrix}] \Rightarrow [\begin{matrix} 3 + 4 & 1 + 10 \\ 9 + 8 & 3 + 20 \end{matrix}] = [\begin{matrix} 7 & 11 \\ k & 23 \end{matrix}] \Rightarrow [\begin{matrix} 7 & 11 \\ 17 & 23 \end{matrix}] = [\begin{matrix} 7 & 11 \\ k & 23 \end{matrix}]$

Now on equating the corresponding elements we get the value of k = 17

For Daily Free Study Material Join wiredfaculty

Matrices

If $[\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}] [\begin{matrix} 3 & 1 \\ 2 & 5 \end{matrix}] = [\begin{matrix} 7 & 11 \\ k & 23 \end{matrix}]$ , then write the value of k.

Some More Questions From Matrices Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction

For Daily Free Study Material Join wiredfaculty

Matrices

If 1 23 4 3 12 5 = 7 11k 23 , then write the value of k.

Some More Questions From Matrices Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

If $[\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}] [\begin{matrix} 3 & 1 \\ 2 & 5 \end{matrix}] = [\begin{matrix} 7 & 11 \\ k & 23 \end{matrix}]$ , then write the value of k.