The value of variable x is -7 in matrix A and y is -25 in matrix B.
What is matrix?
A matrix is a rectangular array or table of numbers,symbols, or
expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.
How to find value of variables?
We are given two matrices A=[tex]\left[\begin{array}{ccc}3&x\\6&1\\-8&5\end{array}\right][/tex] and B=-5A=[tex]\left[\begin{array}{ccc}-15&35\\-30&-5\\40&y\end{array}\right][/tex].
We have to find the value of x and y.
First multiply A with -5 which makes it as under:
-5A=-5[tex]\left[\begin{array}{ccc}3&x\\6&1\\-8&5\end{array}\right][/tex]
-5A=[tex]\left[\begin{array}{ccc}-15&-5x\\-30&-5\\40&-25\end{array}\right][/tex]------------1
Equating 1 & B
[tex]\left[\begin{array}{ccc}-15&-5x\\-30&-5\\40&-25\end{array}\right][/tex]=[tex]\left[\begin{array}{ccc}-15&35\\-30&-5\\40&y\end{array}\right][/tex]
When two matrices are equal to each other then the corresponding elements are also equal to each other.
-5x=35
x=35/-5
x=-7
y=-25
Hence the value of variable x is -7 in matrix A and y=-25 in matrix B.
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