Class 12

Math

Algebra

Matrices

A matrix denotes a number.

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Prove that:[ x y z ] $⎣⎡ ahg hbf gfc ⎦⎤ $$⎣⎡ xyz ⎦⎤ $$=[ax_{2} +by_{2} +cz_{2}+cfz+2gzx+2hxy]$

If the number of elements in a matrix is $60$, then how many different order of matrix are possible?

A square matrix $[a_{ij}]$ such that $a_{ij}=0$ for $i=j$ and $a_{ij}=k$ where $k$ is a constant for $i=j$ is called

(i) If a matrix has 4 elements, what are the possible order it can have?(ii) If a matrix has 4 elements, what are the possible orders it can have?

If A = $⎣⎡ 21−1 321 432 ⎦⎤ $, B = $⎣⎡ 1−10 320 012 ⎦⎤ $ Show that AB $=$ BA.

If $A$ is order $m×n$, $B$ is of order $3×p$ & $C$ is pf order $2×4$ if $AB+C$ is defined, find $m,n$ & $p$

Determine whether the product of the matrices is defined in each case. If so, state the order of the product. MN, where $M=[m_{ij}]_{3×1},N=[n_{ij}]_{1×5}$

The matrix $A=⎣⎡ 100 020 004 ⎦⎤ $ is a/an