SaraNextGen.Com
Updated By SaraNextGen
On March 11, 2024, 11:35 AM

Exercise 3.4 - Chapter 3 Matrices class 12 ncert solutions Maths - SaraNextGen [2024]


Question 1:

Find the inverse of each of the matrices, if it exists.

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6327/Chapter%203_html_m593e88d6.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6327/Chapter%203_html_721edad1.gif

We know that A = IA

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6327/Chapter%203_html_97f2fe0.gif

Question 2:

Find the inverse of each of the matrices, if it exists.

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6328/Chapter%203_html_5e09ef58.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6328/Chapter%203_html_mbd887d9.gif

We know that A = IA

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6328/Chapter%203_html_m2b6878d3.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6328/Chapter%203_html_3e66de25.gif

Question 3:

Find the inverse of each of the matrices, if it exists.

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6330/Chapter%203_html_299bc0b2.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6330/Chapter%203_html_375161dd.gif

We know that A = IA

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6330/Chapter%203_html_m56b66c62.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6330/Chapter%203_html_m6a086adc.gif

Question 4:

Find the inverse of each of the matrices, if it exists.

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6334/Chapter%203_html_m3a47a5f9.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6334/Chapter%203_html_m14192b0a.gif

We know that A = IA

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6334/Chapter%203_html_m3accdbd7.gif

Question 5:

Find the inverse of each of the matrices, if it exists.

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6336/Chapter%203_html_m415af525.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6336/Chapter%203_html_17cb06ca.gif

We know that A = IA

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6336/Chapter%203_html_m2fa8c03.gif

Question 6:

Find the inverse of each of the matrices, if it exists.

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6339/Chapter%203_html_m2d1d7c63.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6339/Chapter%203_html_6ea7b5c2.gif

We know that A = IA

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6339/Chapter%203_html_m615efa69.gif

Question 7:

Find the inverse of each of the matrices, if it exists.

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6341/Chapter%203_html_19f5db80.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6341/Chapter%203_html_m29a0ecf4.gif

We know that A = AI

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6341/Chapter%203_html_2a534b80.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6341/Chapter%203_html_m3e86cdc7.gif

Question 8:

Find the inverse of each of the matrices, if it exists.

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6344/Chapter%203_html_m1cb9f4e4.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6344/Chapter%203_html_m1eebccdb.gif

We know that A = IA

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6344/Chapter%203_html_m6709508e.gif

Question 9:

Find the inverse of each of the matrices, if it exists.

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6346/Chapter%203_html_m3e90f6e5.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6346/Chapter%203_html_47b82bc5.gif

We know that A = IA

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6346/Chapter%203_html_6569ef9f.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6346/Chapter%203_html_6f13bdc0.gif

Question 10:

Find the inverse of each of the matrices, if it exists.

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6349/Chapter%203_html_m57c5a5b6.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6349/Chapter%203_html_37d7cbff.gif

We know that A = AI

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6349/Chapter%203_html_5292618d.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6349/Chapter%203_html_32ee3604.gif

Question 11:

Find the inverse of each of the matrices, if it exists.

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6352/Chapter%203_html_m55510b6a.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6352/Chapter%203_html_21fe3898.gif

We know that A = AI

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6352/Chapter%203_html_m27a2e045.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6352/Chapter%203_html_9d4782.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6352/Chapter%203_html_7986f85d.gif

Question 12:

Find the inverse of each of the matrices, if it exists.

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6355/Chapter%203_html_m708ef6a8.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6355/Chapter%203_html_6c3d4bc3.gif

We know that A = IA

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6355/Chapter%203_html_108326ab.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6355/Chapter%203_html_m3b0072b8.gif

Now, in the above equation, we can see all the zeros in the second row of the matrix on the L.H.S.

Therefore, A−1 does not exist.

Question 13:

Find the inverse of each of the matrices, if it exists.

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6357/Chapter%203_html_4212d6f1.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6357/Chapter%203_html_m26f9b774.gif

We know that A = IA

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6357/Chapter%203_html_m2b622823.gif

Question 14:

Find the inverse of each of the matrices, if it exists.

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6361/Chapter%203_html_325fb007.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6361/Chapter%203_html_3837c75e.gif

We know that A = IA

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6361/Chapter%203_html_m6d1fab30.gif

Applyinghttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6361/Chapter%203_html_m40722fe.gif , we have:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6361/Chapter%203_html_1f4dc87d.gif

Now, in the above equation, we can see all the zeros in the first row of the matrix on the L.H.S.

Therefore, A−1 does not exist.

Question 15:

Find the inverse of each of the matrices, if it exists.

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6364/Chapter%203_html_m7ed155fd.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6364/Chapter%203_html_m2ec31e0b.gif

We know that A = IA

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6364/Chapter%203_html_14118b92.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6364/Chapter%203_html_76034623.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6364/Chapter%203_html_m70d257ad.gif

Question 16:

Find the inverse of each of the matrices, if it exists.

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6369/Chapter%203_html_79f13906.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6369/Chapter%203_html_51907961.gif

We know that A = IA

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6369/Chapter%203_html_3fd13b9.gif

Applying R2 → R2 + 3R1 and R3 → R3 − 2R1, we have:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6369/Chapter%203_html_m7602c1e3.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6369/Chapter%203_html_m386a771e.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6369/Chapter%203_html_m7d47c5d.gif

Question 17:

Find the inverse of each of the matrices, if it exists.

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6371/Chapter%203_html_1c0e9203.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6371/Chapter%203_html_60403dcc.gif

We know that A = IA

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6371/Chapter%203_html_6516330e.gif

Applyinghttps://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6371/Chapter%203_html_6b4c037f.gif , we have:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6371/Chapter%203_html_m7e8d6d3f.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6371/Chapter%203_html_m14145be3.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/232/6371/Chapter%203_html_m7da6c34f.gif

Question 18:

Matrices A and B will be inverse of each other only if

A. AB = BA

C. AB = 0, BA = I

B. AB = BA = 0

D. AB = BA = I

Answer:

Answer: D

We know that if A is a square matrix of order m, and if there exists another square matrix B of the same order m, such that AB = BA = I, then B is said to be the inverse of A. In this case, it is clear that A is the inverse of B.

Thus, matrices A and B will be inverses of each other only if AB = BA = I.

Also Read : Miscellaneous-Exercise-Chapter-3-Matrices-class-12-ncert-solutions-Maths

SaraNextGen