Name: Matrix Multiplication and Associated Properties
Uploaded: 2019-07-19
Duration: 6 min 22 s
Description: We learned the addition and subtraction of matrices. Is it possible to multiply the two matrices? Watch this video and learn to multiply two matrices together.

Question

Find the matrix

A

such that

[\begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}] A = [\begin{matrix} 3 & 3 & 5 \\ 1 & 0 & 1 \end{matrix}]

.

Accepted Answer

Given that,

$[\begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}] A = [\begin{matrix} 3 & 3 & 5 \\ 1 & 0 & 1 \end{matrix}]$

To find : matrix $A$

Now,

Let $A = [\begin{matrix} a & b & c \\ d & e & f \end{matrix}]$

$[\begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}] [\begin{matrix} a & b & c \\ d & e & f \end{matrix}] = [\begin{matrix} 3 & 3 & 5 \\ 1 & 0 & 1 \end{matrix}]$

$[\begin{matrix} 1 \times a + 1 \times d & 1 \times b + 1 \times e & 1 \times c + 1 \times f \\ 0 \times a + 1 \times d & 0 \times b + 1 \times e & 0 \times c + 1 \times f \end{matrix}] = [\begin{matrix} 3 & 3 & 5 \\ 1 & 0 & 1 \end{matrix}]$

$[\begin{matrix} a + d & b + e & c + f \\ d & e & f \end{matrix}] = [\begin{matrix} 3 & 3 & 5 \\ 1 & 0 & 1 \end{matrix}]$

Equating the corresponding terms...

$a + d = 3 . . . . . . . . . . . . . (1) d = 1 . . . . . . . . . (2)$

$a + 1 = 3 \Rightarrow a = 2$

$b + e = 3 . . . . . . . . . (3) e = 0 . . . . . . . . . . . . (4)$

$b + 0 = 3 \Rightarrow b = 3$

$c + f = 5 . . . . . . . . . . . . (5) f = 1 . . . . . . . . . . . . . . . (6)$

$c + 1 = 5 \Rightarrow c = 4$

Hence, matrix is $A = [\begin{matrix} 2 & 3 & 4 \\ 1 & 0 & 1 \end{matrix}]$ .

Find the matrix $A$ such that $[\begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}] A = [\begin{matrix} 3 & 3 & 5 \\ 1 & 0 & 1 \end{matrix}]$ .

Important Questions on Matrices

Learn and Prepare for any exam you want !

Find the matrix A such that 1101A=335101.

Important Questions on Matrices

Learn and Prepare for any exam you want !

Find the matrix $A$ such that $[\begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}] A = [\begin{matrix} 3 & 3 & 5 \\ 1 & 0 & 1 \end{matrix}]$ .