If A= [ ccc 4 & 3 & 2 -1 & 2 & 0 ], B= [ cc 1 & 2 -1 & 0 1 & -2 ]… - Vidyadip

Question

If $A=\left[\begin{array}{ccc}4 & 3 & 2 \\ -1 & 2 & 0\end{array}\right], B=\left[\begin{array}{cc}1 & 2 \\ -1 & 0 \\ 1 & -2\end{array}\right]$, show that matrix $A B$ is non-singular.

✓

Answer

$
\begin{aligned}
& AB =\left[\begin{array}{rrr}
4 & 3 & 2 \\
-1 & 2 & 0
\end{array}\right]\left[\begin{array}{rr}
1 & 2 \\
-1 & 0 \\
1 & -2
\end{array}\right] \\
& =\left[\begin{array}{rr}
4-3+2 & 8+0-4 \\
-1-2+0 & -2+0-0
\end{array}\right]=\left[\begin{array}{rr}
3 & 4 \\
-3 & -2
\end{array}\right] \\
& \therefore| AB |=\left|\begin{array}{rr}
3 & 4 \\
-3 & -2
\end{array}\right| \\
& \quad=-6-(-12)=6 \neq 0
\end{aligned}
$
Hence, $A B$ is a non-singular matrix.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the following Question.(1 Marks)" from Matrices (p-1)→Matrices (p-1) — all question types→Maths (commerce) STD 12 Commerce / Arts question papers→Maharashtra Board STD 12 Commerce / Arts question papers→Maharashtra Board question paper generator→

Similar questions

Write the dual of the following.

13 is prime number and India is a democratic country

Evalute : $\int \frac{1}{\sqrt{3 x^2-5}} d x$

Write the following statements in symbolic form : If Kutub-Minar is in Delhi, then Taj Mahal is in Agra.

Find the order and degree of the following differential equations:
$x+\frac{d y}{d x}=1+\left(\frac{d y}{d x}\right)^2$

Write the following statements in symbolic form.

If Qutub – Minar is in Delhi then Taj-Mahal is in Agra

Determine the truth values of the following statements : x + y = 0 is the equation of a straight line if and only if y2 = 4x is the equation of the parabola.

Write the negation of each of the following statements : 3 is a natural number.

State which of the following sentences are statements in logic : Read a lot to improve your writing skill.

Evalute : $\int \frac{d x}{\sqrt{4 x^2-5}} d x$

State which of the following sentences are statements in logic : Why are you sad?